Journal articles: 'B-spline functions'

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Tsay, D. M., and C. O. Huey. "Application of Rational B-Splines to the Synthesis of Cam-Follower Motion Programs." Journal of Mechanical Design 115, no. 3 (September 1, 1993): 621–26. http://dx.doi.org/10.1115/1.2919235.

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A procedure employing rational B-spline functions for the synthesis of cam-follower motion programs is presented. It differs from earlier techniques that employ spline functions by using rational B-spline basis functions to interpolate motion constraints. These rational B-splines permit greater flexibility in refining motion programs. Examples are provided to illustrate application of the approach.

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Pool, Maryam Khazaei, and Lori Lewis. "A SURVEY ON RECENT HIGHER ORDER SPLINE TECHNIQUES FOR SOLVING BURGERS EQUATION USING B-SPLINE METHODS AND VARIATION OF B-SPLINE TECHNIQUES." Journal of Mathematical Sciences: Advances and Applications 70, no. 1 (April 10, 2022): 1–26. http://dx.doi.org/10.18642/jmsaa_7100122245.

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline finite elements method, Exponential cubic B-spline method, Septic B-spline technique, Quintic B-spline Galerkin method, and B-spline Galerkin method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

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Budakçı, Gülter, and Halil Oruç. "Further Properties of Quantum Spline Spaces." Mathematics 8, no. 10 (October 14, 2020): 1770. http://dx.doi.org/10.3390/math8101770.

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We construct q-B-splines using a new form of truncated power functions. We give basic properties to show that q-B-splines form a basis for quantum spline spaces. On the other hand, we derive algorithmic formulas for 1/q-integration and 1/q-differentiation for q-spline functions. Moreover, we show a way to find the polynomial pieces on each interval of a q-spline function.

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Journal, Baghdad Science. "Solving B- spline functions." Baghdad Science Journal 3, no. 4 (December 3, 2006): 713–21. http://dx.doi.org/10.21123/bsj.3.4.713-721.

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In this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions

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AL-Faour, Omar M. "Solving B- spline functions." Baghdad Science Journal 3, no. 4 (December 1, 2006): 713–21. http://dx.doi.org/10.21123/bsj.2006.758.

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In this paper, we proposed to zoom Volterra equations system Altfazlah linear complementarity of the first type in this approximation were first forming functions notch Baschtdam matrix and then we discussed the approach and stability, to notch functions

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Strelkovskaya, Irina, Irina Solovskaya, and Juliya Strelkovska. "Application of real and complex splines in infocommunication problems." Problemi telekomunìkacìj, no. 1(28) (December 22, 2021): 3–19. http://dx.doi.org/10.30837/pt.2021.1.01.

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The work offers the solution to problems of analysis and synthesis of infocommunication systems with the help of real and complex spline functions. The use of the spline approximation method for solving problems of recovery of random signals and self-similar traffic, management of network objects and network as a whole, and procedures of infocommunication objects and networks functioning is offered. To solve the problems of forecasting, in particular, forecasting the characteristics of network traffic and maintaining the QoS characteristics in its service and formation of requirements for network buffer devices, developed spline extrapolation based on different types of real spline functions, namely: linear, quadratic, quadratic B-splines, cubic, cubic B-splines, cubic Hermite splines. As a criterion for choosing the type of spline function, the prediction error is selected, the accuracy of which can be increased by using a particular kind of spline, depending on the object being predicted. The use of complex flat spline functions is considered to solve the class of user positioning problems in the radio access network. In general, the use of real and complex spline functions allows obtaining the results of improving the Quality of Service in the infocommunication network and ensuring the scalability of the obtained solutions.

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MacCarthy, B. L., and N. D. Burns. "An Evaluation of Spline Functions for use in Cam Design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 3 (July 1985): 239–48. http://dx.doi.org/10.1243/pime_proc_1985_199_118_02.

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This paper shows how spline functions can be employed for kinematic motion specification in cam design. The polynomial spline is introduced as a special case of a continuous piecewise function. Cubic and quintic splines are derived and their properties are discussed in the cam design context. It is shown how standard cam laws can be approximated extremely accurately with a small number of points and appropriate boundary conditions. The modified sinusoidal acceleration cam law is used as an example. The application of quintic splines to non-standard and special motions is discussed. The algebraic and B-spline representations of spline functions are compared. The former is considered preferable in this context and a list of useful algorithms is given. The real power of the spline function, in particular the algebraic quintic spline, is its simplicity, ease of computation and adaptability to non-standard design problems. The use of parametrized, deficient and exponential splines is proposed for specific applications.

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Che, Xiang Jiu, Gerald Farin, Zhan Heng Gao, and Dianne Hansford. "The Product of Two B-Spline Functions." Advanced Materials Research 186 (January 2011): 445–48. http://dx.doi.org/10.4028/www.scientific.net/amr.186.445.

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A method for calculating the product of two B-spline functions is presented. The product is computed by solving a linear system. The coefficient matrix of the system is a Gramian, which guarantees that the system has a unique solution. Every element of the coefficient matrix and the righthand vector of the system is an inner product of B-splines. The inner product can be computed accurately by making use of numerical methods.

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Speleers, Hendrik. "Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines." ACM Transactions on Mathematical Software 48, no. 1 (March 31, 2022): 1–31. http://dx.doi.org/10.1145/3478686.

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Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in Matlab . The implementation supports the construction, differentiation, and visualization of MDTB-splines whose pieces belong to Tchebycheff spaces that are null-spaces of constant-coefficient linear differential operators. The construction relies on an extraction operator that maps local Tchebycheffian Bernstein functions to the MDTB-spline basis of interest.

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Strelkovskaya, Irina, Irina Solovskaya, and Anastasiya Makoganiuk. "Spline-Extrapolation Method in Traﬃc Forecasting in 5G Networks." Journal of Telecommunications and Information Technology 3 (September 30, 2019): 8–16. http://dx.doi.org/10.26636/jtit.2019.134719.

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This paper considers the problem of predicting self-similar traﬃc with a signiﬁcant number of pulsations and the property of long-term dependence, using various spline functions. The research work focused on the process of modeling self-similar traﬃc handled in a mobile network. A splineextrapolation method based on various spline functions (linear, cubic and cubic B-splines) is proposed to predict selfsimilar traﬃc outside the period of time in which packet data transmission occurs. Extrapolation of traﬃc for short- and long-term forecasts is considered. Comparison of the results of the prediction of self-similar traﬃc using various spline functions has shown that the accuracy of the forecast can be improved through the use of cubic B-splines. The results allow to conclude that it is advisable to use spline extrapolation in predicting self-similar traﬃc, thereby recommending this method for use in practice in solving traﬃc prediction-related problems.

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Gomes, Lorrayne, Milena Vieira Lima, Jeferson Corrêa Ribeiro, Andreia Santos Cezário, Eliandra Maria Bianchini Oliveira, Wallacy Barbacena Rosa dos Santos, Tiago Neves Pereira Valente, Crislaine Messias de Souza, and Aline Sousa Camargos. "FUNÇÕES SPLINES APLICADAS EM DADOS DE CRESCIMENTO." COLLOQUIUM AGRARIAE 13, Especial 2 (June 1, 2017): 222–34. http://dx.doi.org/10.5747/ca.2017.v13.nesp2.000229.

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In animal breeding, new methodologies can be applied in statistical analysis to improve the genetic evaluation and, for this reason, they have been the subject in several studies. In the last years, several research works have intended the model development with more adjustable functions to the distinct variables. A set of functions known as Spline functions has called the attention of researches. Then, the purpose of this review is to discuss the use of Spline functions that are applied to growth data in animal breeding. Splines are segmented regression functions that are united by points known as joint points and have the ability to improve the curvature of models and, therefore, the function adjustment. These functions have interesting properties such as the interpolatory nature, less multicolinearity problems, parameter linearity and the ability of increasing the approximation domain, all of which provide estimates in a wide range of possible values. There are three types of Spline functions: natural spline functions, smoothing spline 223 Colloquium Agrariae, vol. 13, n. Especial 2, Jan–Jun, 2017, p. 222-234. ISSN: 1809-8215. DOI: 10.5747/ca.2017.v13.nesp2.000229 functions or nonparametric regression and B-splines functions. These latter functions are more applied to animal breeding, mainly as alternatives to random regression models (RRM) that use the Legendre polynomials. The matrices formed by RRMs with the use of B-spline functions or Legendre polynomials are more scarce and easier to be inverted. Then, the use of Spline functions has been more intensified in the last years because studies have had the purpose of improving the adjustment with less model parameters in functions. New studies will allow improving the methodology and finding out new applications to the Spline functions.

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Toraichi, K., M. Kamada, S. Itahashi, and R. Mori. "Window functions represented by B-spline functions." IEEE Transactions on Acoustics, Speech, and Signal Processing 37, no. 1 (January 1989): 145–47. http://dx.doi.org/10.1109/29.17517.

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Rajashekar, Naraveni, Sudhakar Chaudhary, and V. V. K. Srinivas Kumar. "Approximation of p-Biharmonic Problem using WEB-Spline based Mesh-Free Method." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 6 (October 25, 2019): 703–12. http://dx.doi.org/10.1515/ijnsns-2018-0298.

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Abstract We describe and analyze the weighted extended b-spline (WEB-Spline) mesh-free finite element method for solving the p-biharmonic problem. The WEB-Spline method uses weighted extended b-splines as basis functions on regular grids and does not require any mesh generation which eliminates a difficult, time consuming preprocessing step. Accurate approximations are possible with relatively low-dimensional subspaces. We perform some numerical experiments to demonstrate the efficiency of the WEB-Spline method.

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Tsay, Der Min, and Guan Shyong Hwang. "The Synthesis of Follower Motions of Camoids Using Nonparametric B-Splines." Journal of Mechanical Design 118, no. 1 (March 1, 1996): 138–43. http://dx.doi.org/10.1115/1.2826845.

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This paper proposes a tool to synthesize the motion functions of the camoid-follower mechanisms. The characteristics of these kinds of motion functions are that they possess two independent parameters. To implement the work, this study applies the nonparametric B-spline surface interpolation, whose spline functions are constructed by the closed periodic B-splines and the de Boor’s knot sequences in the two parametric directions of the motion function, respectively. The rules and the restrictions needed to be noticed in the process of synthesis are established. Numerical examples are also given to verify the feasibility of the proposed method.

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Wan, Neng, Ke Du, Tao Chen, Sentang Zhang, and Gongnan Xie. "Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/350682.

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In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.

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Duan, Jiwei, and P. K. K. Lee. "Construction of boundary B-spline functions." Computers & Structures 78, no. 5 (December 2000): 737–43. http://dx.doi.org/10.1016/s0045-7949(00)00046-8.

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Gondegaon, Sangamesh, and Hari K. Voruganti. "Spline Parameterization of Complex Planar Domains for Isogeometric Analysis." Journal of Theoretical and Applied Mechanics 47, no. 1 (March 1, 2017): 18–35. http://dx.doi.org/10.1515/jtam-2017-0002.

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Abstract Isogeometric Analysis (IGA) involves unification of modelling and analysis by adopting the same basis functions (splines), for both. Hence, spline based parametric model is the starting step for IGA. Representing a complex domain, using parametric geometric model is a challenging task. Parameterization problem can be defined as, finding an optimal set of control points of a B-spline model for exact domain modelling. Also, the quality of parameterization, too has significant effect on IGA. Finding the B-spline control points for any given domain, which gives accurate results is still an open issue. In this paper, a new planar B-spline parameterization technique, based on domain mapping method is proposed. First step of the methodology is to map an input (non-convex) domain onto a unit circle (convex) with the use of harmonic functions. The unique properties of harmonic functions: global minima and mean value property, ensures the mapping is bi-jective and with no self-intersections. Next step is to map the unit circle to unit square to make it apt for B-spline modelling. Square domain is re-parameterized by using conventional centripetal method. Once the domain is properly parameterized, the required control points are computed by solving the B-spline tensor product equation. The proposed methodology is validated by applying the developed B-spline model for a static structural analysis of a plate, using isogeometric analysis. Different domains are modelled to show effectiveness of the given technique. It is observed that the proposed method is versatile and computationally efficient.

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Majeed, Abdul, Muhammad Abbas, Faiza Qayyum, Kenjiro T. Miura, Md Yushalify Misro, and Tahir Nazir. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter." Mathematics 8, no. 12 (November 24, 2020): 2102. http://dx.doi.org/10.3390/math8122102.

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Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

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Janecki, Dariusz, Leszek Cedro, and Jarosław Zwierzchowski. "Separation Of Non-Periodic And Periodic 2D Profile Features Using B-Spline Functions." Metrology and Measurement Systems 22, no. 2 (June 1, 2015): 289–302. http://dx.doi.org/10.1515/mms-2015-0016.

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Abstract The form, waviness and roughness components of a measured profile are separated by means of digital filters. The aim of analysis was to develop an algorithm for one-dimensional filtering of profiles using approximation by means of B-splines. The theory of B-spline functions introduced by Schoenberg and extended by Unser et al. was used. Unlike the spline filter proposed by Krystek, which is described in ISO standards, the algorithm does not take into account the bending energy of a filtered profile in the functional whose minimization is the principle of the filter. Appropriate smoothness of a filtered profile is achieved by selecting an appropriate distance between nodes of the spline function. In this paper, we determine the Fourier transforms of the filter impulse response at different impulse positions, with respect to the nodes. We show that the filter cutoff length is equal to half of the node-to-node distance. The inclination of the filter frequency characteristic in the transition band can be adjusted by selecting an appropriate degree of the B-spline function. The paper includes examples of separation of 2D roughness, as well as separation of form and waviness of roundness profiles.

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Vijayakumar, Hannah. "Two-piece Cubic Spline Functions." Mapana - Journal of Sciences 2, no. 1 (October 2, 2003): 25–33. http://dx.doi.org/10.12723/mjs.3.2.

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.M Prenter defines a cubic Spline function in an interval [a, b] as a piecewise cubic polynomial which is twice continuously differentiable in the entire interval [a, b]. The smooth cubic spline functions fitting the given data are the most popular spline functions and when used for interpolation, they do not have the oscillatory behavior which characterized high-degree polynomials. The natural spline has been shown to be unique function possessing the minimum curvature property of all functions interpolating the data and having square integrable second derivative. In this sense, the natural cubic spline is the smoothest function which interpolates the data. Here Two-piece Natural Cubic Spline functions have been defined. An approximation with no indication of its accuracy is utterly valueless. Where an approximation is intended for the general use, one must , of course, go for the trouble of estimating the error as precisely as possible. In this section, an attempt has been made to derive closed form expressions for the error-functions in the case of Two-piece Spline Functions.

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Zhao, Yanchun, Mengzhu Zhang, Qian Ni, and Xuhui Wang. "Adaptive Nonparametric Density Estimation with B-Spline Bases." Mathematics 11, no. 2 (January 5, 2023): 291. http://dx.doi.org/10.3390/math11020291.

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Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can improve on the approximation capability of uniform B-splines. Based on this observation, we perform density estimation with nonuniform B-splines. By introducing the error indicator attached to each interval, we propose an adaptive strategy to generate the nonuniform knot vector. The error indicator is an approximation of the information entropy locally, which is closely related to the number of kernels when we construct the nonuniform estimator. The numerical experiments show that, compared with the uniform B-spline, the local density estimation with nonuniform B-splines not only achieves better estimation results but also effectively alleviates the overfitting phenomenon caused by the uniform B-splines. The comparison with the existing estimation procedures, including the state-of-the-art kernel estimators, demonstrates the accuracy of our new method.

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Hernández, V., J. Estrada, E. Moreno, S. Rodríguez, and A. Mansur. "Numerical Solution of a Wave Propagation Problem Along Plate Structures Based on the Isogeometric Approach." Journal of Theoretical and Computational Acoustics 26, no. 01 (March 2018): 1750030. http://dx.doi.org/10.1142/s259172851750030x.

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Ultrasonic guided waves propagating along large structures have great potential as a nondestructive evaluation method. In this context, it is very important to obtain the dispersion curves, which depend on the cross-section of the structure. In this paper, we compute dispersion curves along infinite isotropic plate-like structures using the semi-analytical method (SAFEM) with an isogeometric approach based on B-spline functions. The SAFEM method leads to a family of generalized eigenvalue problems depending on the wave number. For a prescribed wave number, the solution of this problem consists of the nodal displacement vector and the frequency of the guided wave. In this work, the results obtained with B-splines shape functions are compared to the numerical SAFEM solution with quadratic Lagrange shape functions. Advantages of the isogeometric approach are highlighted and include the smoothness of the displacement field components and the computational cost of solving the corresponding generalized eigenvalue problems. Finally, we investigate the convergence of Lagrange and B-spline approaches when the number of degrees of freedom grows. The study shows that cubic B-spline functions provide the best solution with the smallest relative errors for a given number of degrees of freedom.

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Jiwari, Ram, and Ali Saleh Alshomrani. "A new algorithm based on modified trigonometric cubic B-splines functions for nonlinear Burgers’-type equations." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 8 (August 7, 2017): 1638–61. http://dx.doi.org/10.1108/hff-05-2016-0191.

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Purpose The main aim of the paper is to develop a new B-splines collocation algorithm based on modified cubic trigonometric B-spline functions to find approximate solutions of nonlinear parabolic Burgers’-type equations with Dirichlet boundary conditions. Design/methodology/approach A modification is made in cubic trigonometric B-spline functions to handle the Dirichlet boundary conditions and an algorithm is developed with the help of modified cubic trigonometric B-spline functions. The proposed algorithm reduced the Burgers’ equations into a system of first-order nonlinear ordinary differential equations in time variable. Then, strong stability preserving Runge-Kutta 3rd order (SSP-RK3) scheme is used to solve the obtained system. Findings A different technique based on modified cubic trigonometric B-spline functions is proposed which is quite different from to the schemes developed in Abbas et al. (2014) and Nazir et al. (2016), and the developed algorithms are free from linearization process and finite difference operators. Originality/value To the best knowledge of the authors, this technique is novel for solving nonlinear partial differential equations, and the new proposed technique gives better results than the results discussed in Ozis et al. (2003), Kutluay et al. (1999), Khater et al. (2008), Korkmaz and Dag (2011), Kutluay et al. (2004), Rashidi et al. (2009), Mittal and Jain (2012), Mittal and Jiwari (2012), Mittal and Tripathi (2014), Xie et al. (2008) and Kadalbajoo et al. (2005).

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SAVACI, F. A., and M. GÜNGÖR. "ESTIMATING PROBABILITY DENSITY FUNCTIONS AND ENTROPIES OF CHUA'S CIRCUIT USING B-SPLINE FUNCTIONS." International Journal of Bifurcation and Chaos 22, no. 05 (May 2012): 1250107. http://dx.doi.org/10.1142/s0218127412501076.

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In this paper, first the probability density functions (PDFs) of the states of Chua's circuit have been estimated using B-spline functions and then the state entropies of Chua's circuit with respect to the bifurcation parameter have been obtained. The results of the proposed B-spline density estimator have been compared with the results obtained from the Parzen density estimator.

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ZHENG, TIANXIANG, and LIHUA YANG. "B-SPLINE ANALYTICAL REPRESENTATION OF THE MEAN ENVELOPE FOR EMPIRICAL MODE DECOMPOSITION." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 02 (March 2010): 175–95. http://dx.doi.org/10.1142/s0219691310003420.

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This paper investigates how the mean envelope, the subtrahend in the sifting procedure for the Empirical Mode Decomposition (EMD) algorithm, represents as an expansion in terms of basis. To this end, a novel approach that gives an alternative analytical expression using B-spline functions is presented. The basic concept lies mainly on the idea that B-spline functions form a basis for the space of splines and have refined-node representations by knot insertion. This newly-developed expression is essentially equivalent to the conventional one, but gives a more explicit formulation on this issue. For the purpose of establishing the mathematical foundation of the EMD methodology, this study may afford a favorable opportunity in this direction.

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Afzal, Arfan Raheen, Cheng Dong, and Xuewen Lu. "Estimation of partly linear additive hazards model with left-truncated and right-censored data." Statistical Modelling 17, no. 6 (June 30, 2017): 423–48. http://dx.doi.org/10.1177/1471082x17705993.

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In this article, we consider an additive hazards semiparametric model for left-truncated and right-censored data where the risk function has a partly linear structure, we call it the partly linear additive hazards model. The nonlinear components are assumed to be B-splines functions, so the model can be viewed as a semiparametric model with an unknown baseline hazard function and a partly linear parametric risk function, which can model both linear and nonlinear covariate effects, hence is more flexible than a purely linear or nonlinear model. We construct a pseudo-score function to estimate the coefficients of the linear covariates and the B-spline basis functions. The proposed estimators are asymptotically normal under the assumption that the true nonlinear functions are B-spline functions whose knot locations and number of knots are held fixed. On the other hand, when the risk functions are unknown non-parametric functions, the proposed method provides a practical solution to the underlying inference problems. We conduct simulation studies to empirically examine the finite-sample performance of the proposed method and analyze a real dataset for illustration.

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Meyer, K. "Advances in methodology for random regression analyses." Australian Journal of Experimental Agriculture 45, no. 8 (2005): 847. http://dx.doi.org/10.1071/ea05040.

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Random regression analyses have become standard methodology for the analysis of traits with repeated records that are thought of as representing points on a trajectory. Modelling curves as a regression on functions of a continuous covariable, such as time, for each individual, random regression models are readily implemented in standard, linear mixed model analyses. Early applications have made extensive use of regressions on orthogonal polynomials. Recently, spline functions have been considered as an alternative. The use of a particular type of spline function, the so-called B-splines, as basis functions for random regression analyses is outlined, emphasising the local influence of individual observations and low degree of polynomials employed. While such analyses are likely to involve more regression coefficients than polynomial models, it is demonstrated that reduced rank estimation via the leading principal components is feasible and likely to yield more parsimonious models and more stable estimates than full rank analyses. The combined application of B-spline basis function and reduced rank estimation is illustrated for a small set of data for beef cattle.

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Nosrati Sahlan, Monireh. "Convergence of approximate solution of mixed Hammerstein type integral equations." Boletim da Sociedade Paranaense de Matemática 38, no. 2 (February 19, 2018): 61–74. http://dx.doi.org/10.5269/bspm.v38i2.38043.

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In the present paper, a computational method for solving nonlinear Volterra-Fredholm Hammerestein integral equations is proposed by using compactly supported semiorthogonal cubic B-spline wavelets as basis functions. Dual functions and Operational matrices of B-spline wavelets via Galerkin method are utilized to reduce the computation of integral equations to some algebraic system, where in the Galerkin method dual of B-spline wavelets are applied as weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.

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Wang, Zhihua, Falai Chen, and Jiansong Deng. "Evaluation Algorithm of PHT-Spline Surfaces." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (September 12, 2017): 760–74. http://dx.doi.org/10.4208/nmtma.2017.0003.

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AbstractPHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline locally in a tensor product B-spline, and then apply the de-Boor algorithm to evaluate the PHT-spline at a certain parameter pair. We perform analysis about computational complexity and memory costs. The results show that our algorithm takes about the same order of computational costs while requires much less amount of memory compared with the Bézier representations. We give an example to illustrate the effectiveness of our algorithm.

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Vivas-Cortez, Miguel, M. J. Huntul, Maria Khalid, Madiha Shafiq, Muhammad Abbas, and Muhammad Kashif Iqbal. "Application of an Extended Cubic B-Spline to Find the Numerical Solution of the Generalized Nonlinear Time-Fractional Klein–Gordon Equation in Mathematical Physics." Computation 12, no. 4 (April 11, 2024): 80. http://dx.doi.org/10.3390/computation12040080.

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A B-spline function is a series of flexible elements that are managed by a set of control points to produce smooth curves. By using a variety of points, these functions make it possible to build and maintain complicated shapes. Any spline function of a certain degree can be expressed as a linear combination of the B-spline basis of that degree. The flexibility, symmetry and high-order accuracy of the B-spline functions make it possible to tackle the best solutions. In this study, extended cubic B-spline (ECBS) functions are utilized for the numerical solutions of the generalized nonlinear time-fractional Klein–Gordon Equation (TFKGE). Initially, the Caputo time-fractional derivative (CTFD) is approximated using standard finite difference techniques, and the space derivatives are discretized by utilizing ECBS functions. The stability and convergence analysis are discussed for the given numerical scheme. The presented technique is tested on a variety of problems, and the approximate results are compared with the existing computational schemes.

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Tanaka, Satoyuki, and Hiroshi Okada. "An Adaptive Wavelet Finite Element Method with High-Order B-Spline Basis Functions." Key Engineering Materials 345-346 (August 2007): 877–80. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.877.

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In this paper, an adaptive strategy based on a B-spline wavelet Galerkin method is discussed. The authors have developed the wavelet Galerkin Method which utilizes quadratic and cubic B-spline scaling function/wavelet as its basis functions. The developed B-spline Galerkin Method has been proven to be very accurate in the analyses of elastostatics. Then the authors added a capability to adaptively adjust the special resolution of the basis functions by adding the wavelet basis functions where the resolution needs to be enhanced.

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Sana, Madiha, and Muhammad Mustahsan. "Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines." Mathematics 7, no. 5 (May 20, 2019): 452. http://dx.doi.org/10.3390/math7050452.

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In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence analysis is also performed by some numerical examples.

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Li, Hongyi, Chaojie Wang, and Di Zhao. "An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/150127.

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A B-spline empirical mode decomposition (BEMD) method is proposed to improve the celebrated empirical mode decomposition (EMD) method. The improvement of BEMD on EMD mainly concentrates on the sifting process. First, instead of the curve that resulted from computing the average of upper and lower envelopes, the curve interpolated by the midpoints of local maximal and minimal points is used as the mean curve, which can reduce the cost of computation. Second, the cubic spline interpolation is replaced with cubic B-spline interpolation on account of the advantages of B-spline over polynomial spline. The effectiveness of BEMD compared with EMD is validated by numerical simulations and an application to find the basis functions of EMI signals.

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Kano, Hiroyuki, Hiroaki Nakata, and Clyde F. Martin. "Optimal Design of Curves by B-Spline Functions." Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications 2002 (May 5, 2002): 164–69. http://dx.doi.org/10.5687/sss.2002.164.

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Panda, Rutuparna, and B. N. Chatterji. "B-spline signal processing using harmonic basis functions." Signal Processing 72, no. 3 (February 1999): 147–66. http://dx.doi.org/10.1016/s0165-1684(98)00176-5.

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Ke, Ruan, Xia De-lin, and Yan Pu-liu. "Fingerprint representation methods based on B-Spline functions." Wuhan University Journal of Natural Sciences 9, no. 2 (March 2004): 193–97. http://dx.doi.org/10.1007/bf02830601.

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Zong, Z., and K. Y. Lam. "Estimation of complicated distributions using B-spline functions." Structural Safety 20, no. 4 (December 1998): 341–55. http://dx.doi.org/10.1016/s0167-4730(98)00019-8.

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Watkins, L. R., and J. Le Bihan. "Fast, accurate interpolation with B-spline scaling functions." Electronics Letters 30, no. 13 (June 23, 1994): 1024–25. http://dx.doi.org/10.1049/el:19940704.

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Zürnacı, Fatma, and Çetin Di̇şi̇büyük. "Non-polynomial divided differences and B-spline functions." Journal of Computational and Applied Mathematics 349 (March 2019): 579–92. http://dx.doi.org/10.1016/j.cam.2018.09.026.

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POLGÁR, Rudolf, and Zoltán PÁSZTORY. "History of Spline Functions and Application in Wood Industry Part 1." Wood Science = Faipar 63, no. 2 (October 30, 2015): 1–8. http://dx.doi.org/10.14602/woodsci.2015.2.29.

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<p class="p1">Tanulmányunkkal szeretnénk bepillantást adni a spline függvény felfedezésének történetétől a jelenleg alkalmazott módszerekig. Első cikkünk foglalkozik a spline függvények feltalálásával és az elmúlt évszázadokban történt fejlődésükkel. A látszólag száraz matematikai képletekben megjelenő függvények nagyon gyakorlatias megoldások, éppen ezért a mai terméktervezés egyik fő eszközei. A különböző spline típusokat mutatjuk be, mint a Bézier-spline, az interpolációs spline, a B- és a T-spline, valamint a NURBS felületképzési módszerek. Az elmúlt évtizedekben fokozódó ipari verseny és az informatikai technológiák fejlődése kedvező környezetet biztosított a spline függvények fejlődéséhez és széleskörű alkalmazásához. Jelen cikk megadja a spline függvények matematikai formuláit a hasznosítás számára, a következő cikk pedig az ipari alkalmazásba, kiemelten a faipari alkalmazásokba ad betekintést.</p>

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Goss, Andreas, Manuel Hernández-Pajares, Michael Schmidt, David Roma-Dollase, Eren Erdogan, and Florian Seitz. "High-Resolution Ionosphere Corrections for Single-Frequency Positioning." Remote Sensing 13, no. 1 (December 22, 2020): 12. http://dx.doi.org/10.3390/rs13010012.

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The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.

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Mittal, R. C., and Rachna Bhatia. "Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method." International Journal of Partial Differential Equations 2014 (August 10, 2014): 1–8. http://dx.doi.org/10.1155/2014/343497.

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Modified cubic B-spline collocation method is discussed for the numerical solution of one-dimensional nonlinear sine-Gordon equation. The method is based on collocation of modified cubic B-splines over finite elements, so we have continuity of the dependent variable and its first two derivatives throughout the solution range. The given equation is decomposed into a system of equations and modified cubic B-spline basis functions have been used for spatial variable and its derivatives, which gives results in amenable system of ordinary differential equations. The resulting system of equation has subsequently been solved by SSP-RK54 scheme. The efficacy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and are in good agreement with earlier studies.

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RASHIDINIA, J., and ALI PARSA. "SEMI-ORTHOGONAL SPLINE SCALING FUNCTIONS FOR SOLVING HAMMERSTEIN INTEGRAL EQUATIONS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 03 (May 2011): 427–43. http://dx.doi.org/10.1142/s0219691311004134.

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We developed a new numerical procedure based on the quadratic semi-orthogonal B-spline scaling functions for solving a class of nonlinear integral equations of the Hammerstein-type. Properties of the B-spline wavelet method are utilized to reduce the Hammerstein equations to some algebraic equations. The advantage of our method is that the dimension of the arising algebraic equation is 10 × 10. The operational matrix of semi-orthogonal B-spline scaling functions is sparse which is easily applicable. Error estimation of the presented method is analyzed and proved. To demonstrate the validity and applicability of the technique the method applied to some illustrative examples and the maximum absolute error in the solutions are compared with the results in existing methods.20,25,27,29

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Yanhua, Tan, and Li Hongxing. "Faired MISO B-Spline Fuzzy Systems and Its Applications." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/870595.

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We construct two classes of faired MISO B-spline fuzzy systems using the fairing method in computer-aided geometric design (CAGD) for reducing adverse effects of the inexact data. Towards this goal, we generalize the faring method to high-dimension cases so that the faring method only for SISO and DISO B-spline fuzzy systems is extended to fair the MISO ones. Then the problem to construct a faired MISO B-spline fuzzy systems is transformed into solving an optimization problem with a strictly convex quadratic objective function and the unique optimal solution vector is taken as linear combination coefficients of the basis functions for a certain B-spline fuzzy system to obtain a faired MISO B-spline fuzzy system. Furthermore, we design variable universe adaptive fuzzy controllers by B-spline fuzzy systems and faired B-spline fuzzy systems to stabilize the double inverted pendulum. The simulation results show that the controllers by faired B-spline fuzzy systems perform better than those by B-spline fuzzy systems, especially when the data for fuzzy systems are inexact.

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GU, JINLIANG, JIANMING ZHANG, and XIAOMIN SHENG. "THE BOUNDARY FACE METHOD WITH VARIABLE APPROXIMATION BY B-SPLINE BASIS FUNCTION." International Journal of Computational Methods 09, no. 01 (March 2012): 1240009. http://dx.doi.org/10.1142/s0219876212400099.

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B-spline basis functions as a new approximation method is introduced in the boundary face method (BFM) to obtain numerical solutions of 3D potential problems. In the BFM, both boundary integration and variable approximation are performed in the parametric spaces of the boundary surfaces, therefore, keeps the exact geometric information of a body in which the problem is defined. In this paper, local bivariate B-spline functions are proposed to alleviate the influence of B-spline tensor product that will deteriorate the exactness of numerical results. Numerical tests show that the new method has well performance in both exactness and convergence.

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Liu, Yanan. "ICCM2016: Multi-Patch-Based B-Spline Method for Solid and Structure." International Journal of Computational Methods 17, no. 10 (January 31, 2020): 2050005. http://dx.doi.org/10.1142/s021987622050005x.

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In this paper, the solution domain is divided into multi-patches on which B-spline basis functions are used for approximation. The different B-spline patches are connected by a transition region which is described by several elements. The basis functions in different B-spline patches are modified in the transition region to ensure the basic polynomial reconstruction condition and the compatibility of displacements and their gradients. This new method is applied to the stress analysis of 2D elasticity problems in order to investigate its performance. Numerical results show that the present method is accurate and stable.

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Cano, G., M. Blanco, I. Casasús, X. Cortés-Lacruz, and D. Villalba. "Comparison of B-splines and non-linear functions to describe growth patterns and predict mature weight of female beef cattle." Animal Production Science 56, no. 11 (2016): 1787. http://dx.doi.org/10.1071/an15089.

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The objective of this study was to compare the ability of Basis spline (B-spline) models and five non-linear functions (Richards, Brody, Von Bertalanffy, Gompertz and Logistic) to describe the growth of females of a beef cattle breed and predict cow mature weight (A). Random regression models that included animal variation within function parameters were fitted using mixed model procedures. Comparisons were made among these functions for goodness of fit, standardised residuals and biological interpretability of the growth curve parameters. The B-spline function showed the best goodness of fit and within non-linear functions, the Richards and Von Bertalanffy functions estimated bodyweight at different periods accurately. The method of fitting the residual variance that provided the best goodness of fit in the model was the constant plus power variance function. The Richards function was found to be the best non-linear function and was compared with the B-spline function to predict mature weight. When the A parameter was estimated using fixed effects, it had a low correlation with the actual mature weight of the cow and the use of this estimate yielded no more gain in predictive accuracy of mature weight than the use of average breed mature weight. When A was estimated using fixed and random effects, it had a moderate correlation with actual mature weight for the B-spline and Richards functions. The use of both types of effects to estimate the maturity index reduced the error compared with the use of average mature weight, especially for the B-spline function, which is recommended as the best function to describe animal growth and predict mature weight.

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Cano, G., M. Blanco, I. Casasús, X. Cortés-Lacruz, and D. Villalba. "Corrigendum to: Comparison of B-splines and non-linear functions to describe growth patterns and predict mature weight of female beef cattle." Animal Production Science 56, no. 12 (2016): 2161. http://dx.doi.org/10.1071/an15089_co.

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The objective of this study was to compare the ability of Basis spline (B-spline) models and five non-linear functions (Richards, Brody, Von Bertalanffy, Gompertz and Logistic) to describe the growth of females of a beef cattle breed and predict cow mature weight (A). Random regression models that included animal variation within function parameters were fitted using mixed model procedures. Comparisons were made among these functions for goodness of fit, standardised residuals and biological interpretability of the growth curve parameters. The B-spline function showed the best goodness of fit and within non-linear functions, the Richards and Von Bertalanffy functions estimated bodyweight at different periods accurately. The method of fitting the residual variance that provided the best goodness of fit in the model was the constant plus power variance function. The Richards function was found to be the best non-linear function and was compared with the B-spline function to predict mature weight. When the A parameter was estimated using fixed effects, it had a low correlation with the actual mature weight of the cow and the use of this estimate yielded no more gain in predictive accuracy of mature weight than the use of average breed mature weight. When A was estimated using fixed and random effects, it had a moderate correlation with actual mature weight for the B-spline and Richards functions. The use of both types of effects to estimate the maturity index reduced the error compared with the use of average mature weight, especially for the B-spline function, which is recommended as the best function to describe animal growth and predict mature weight.

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Wang, Shitong, and Hongjun Lu. "Fuzzy System and CMAC Network with B-Spline Membership/Basis Functions can Approximate A Smooth Function and its Derivatives." International Journal of Computational Intelligence and Applications 03, no. 03 (September 2003): 265–79. http://dx.doi.org/10.1142/s1469026803000963.

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In control and other modeling applications, fuzzy system with B-spline membership functions and CMAC neural network with B-spline basis functions are sometimes desired to approximate not only the assigned smooth function as well as its derivatives. In this paper, by designing the fuzzy system and CMAC neural network with B-spline basis functions, we prove that such a fuzzy system and CMAC can universally approximate a smooth function and its derivatives, that is to say, for a given accuracy, we can approximate an arbitrary smooth function by such fuzzy system and CMAC that not only the function is approximated within this accuracy, but its derivatives are approximated as well. The conclusions here provide solid theoretical foundation for their extensive applications.

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Yaseen, Muhammad, Qamar Un Nisa Arif, Reny George, and Sana Khan. "Comparative Numerical Study of Spline-Based Numerical Techniques for Time Fractional Cattaneo Equation in the Sense of Caputo–Fabrizio." Fractal and Fractional 6, no. 2 (January 18, 2022): 50. http://dx.doi.org/10.3390/fractalfract6020050.

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This study focuses on numerically addressing the time fractional Cattaneo equation involving Caputo–Fabrizio derivative using spline-based numerical techniques. The splines used are the cubic B-splines, trigonometric cubic B-splines and extended cubic B-splines. The space derivative is approximated using B-splines basis functions, Caputo–Fabrizio derivative is discretized, using a finite difference approach. The techniques are also put through a stability analysis to verify that the errors do not pile up. The proposed scheme’s convergence analysis is also explored. The key advantage of the schemes is that the approximation solution is produced as a smooth piecewise continuous function, allowing us to approximate a solution at any place in the domain of interest. A numerical study is performed using various splines, and the outcomes are compared to demonstrate the efficiency of the proposed schemes.

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Journal articles on the topic 'B-spline functions'

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