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Journal articles on the topic 'Approximation technique'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Geer, James F., and Carl M. Andersen. "Hybrid Pade´-Galerkin Technique for Differential Equations." Applied Mechanics Reviews 46, no. 11S (1993): S255—S265. http://dx.doi.org/10.1115/1.3122644.

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A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade´ expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter ε associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade´ approximation in the form of a rational function

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2

Benammar, Mohieddine, Abdulrahman Alassi, Adel Gastli, Lazhar Ben-Brahim, and Farid Touati. "New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications." Sensors 19, no. 23 (2019): 5148. http://dx.doi.org/10.3390/s19235148.

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Fast and accurate arctangent approximations are used in several contemporary applications, including embedded systems, signal processing, radar, and power systems. Three main approximation techniques are well-established in the literature, varying in their accuracy and resource utilization levels. Those are the iterative coordinate rotational digital computer (CORDIC), the lookup tables (LUTs)-based, and the rational formulae techniques. This paper presents a novel technique that combines the advantages of both rational formulae and LUT approximation methods. The new algorithm exploits the pse

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Worden, Lee, Ira B. Schwartz, Simone Bianco, Sarah F. Ackley, Thomas M. Lietman, and Travis C. Porco. "Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics." Computational and Mathematical Methods in Medicine 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4253167.

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We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of t

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Easterday, Kenneth, and Tommy Smith. "A Monte Carlo Application to Approximate Pi." Mathematics Teacher 84, no. 5 (1991): 387–90. http://dx.doi.org/10.5951/mt.84.5.0387.

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Instruction in the concept of area begins in elementary school and continues through college calculus. Students learn to apply formulas for certain plane figures and later, integration techniques. For figures that are not “nice” shapes or for “irregular” functions, students are taught approximation techniques, which range from counting squares in middle school to trigonometric approximations in high school and various methods of calculus. The purpose of this article is to offer the use of the Monte Carlo procedure on the microcomputer as an alternative tool for approximating areas. One of the

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Jiang, Hui, and Qingshan Yang. "Asymptotic behavior of the weak approximation to a class of Gaussian processes." Journal of Applied Probability 58, no. 3 (2021): 693–707. http://dx.doi.org/10.1017/jpr.2020.110.

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AbstractWe study, under mild conditions, the weak approximation constructed from a standard Poisson process for a class of Gaussian processes, and establish its sample path moderate deviations. The techniques consist of a good asymptotic exponential approximation in moderate deviations, the Besov–Lèvy modulus embedding, and an exponential martingale technique. Moreover, our results are applied to the weak approximations associated with the moving average of Brownian motion, fractional Brownian motion, and an Ornstein–Uhlenbeck process.

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Chen, Jing-Bo, Hong Liu, and Zhi-Fu Zhang. "A separable-kernel decomposition method for approximating the DSR continuation operator." GEOPHYSICS 72, no. 1 (2007): S25—S31. http://dx.doi.org/10.1190/1.2399368.

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We develop a separable-kernel decomposition method for approximating the double-square-root (DSR) continuation operator in one-way migrations in this paper. This new approach is a further development of separable approximations of the single-square-root (SSR) operator. The separable approximation of the DSR operator generally involves solving a complicated nonlinear system of integral equations. Instead of solving this nonlinear system directly, our new method consists of repeatedly applying the separable-kernel technique developed for the two-variable SSR operator to the multivariable DSR ope

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Seke, J., A. V. Soldatov, and N. N. Bogolubov. "Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method." Modern Physics Letters B 11, no. 06 (1997): 245–58. http://dx.doi.org/10.1142/s0217984997000311.

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Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbit

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8

Muresan, Cristina I., Isabela R. Birs, Ovidiu Prodan, Ioan Nascu, and Robin De Keyser. "Approximation Methods for FO-IMC Controllers for Time Delay Systems." E3S Web of Conferences 115 (2019): 01003. http://dx.doi.org/10.1051/e3sconf/201911501003.

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Fractional Order Internal Model Control (FO-IMC) is among the newest trends in extending fractional calculus to the integer order control. Approximation of the FO-IMC is one of the key problems. Apart from this, when dealing with time delay systems, the time delay needs also to be approximated. All these approximations can alter the closed loop performance of the controller. In this paper, FO-IMC controllers will be tested in terms of the approximation accuracy. The case study is a first order system with time delay. Several scenarios will be considered, aiming for a conclusion regarding the c

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9

Payne, Joshua L., and Margaret J. Eppstein. "Pair Approximations of Takeover Dynamics in Regular Population Structures." Evolutionary Computation 17, no. 2 (2009): 203–29. http://dx.doi.org/10.1162/evco.2009.17.2.203.

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In complex adaptive systems, the topological properties of the interaction network are strong governing influences on the rate of flow of information throughout the system. For example, in epidemiological models, the structure of the underlying contact network has a pronounced impact on the rate of spread of infectious disease throughout a population. Similarly, in evolutionary systems, the topology of potential mating interactions (i.e., population structure) affects the rate of flow of genetic information and therefore affects selective pressure. One commonly employed method for quantifying

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10

Alzakari, Sarah A., and Poorvi L. Vora. "Partly-Pseudo-Linear Cryptanalysis of Reduced-Round Speck." Cryptography 5, no. 1 (2020): 1. http://dx.doi.org/10.3390/cryptography5010001.

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We apply McKay’s pseudo-linear approximation of addition modular 2n to lightweight ARX block ciphers with large words, specifically the Speck family. We demonstrate that a pseudo-linear approximation can be combined with a linear approximation using the meet-in-the-middle attack technique to recover several key bits. Thus we illustrate improvements to Speck linear distinguishers based solely on Cho–Pieprzyk approximations by combining them with pseudo-linear approximations, and propose key recovery attacks.

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11

Zhu, Song-Ping, and Guang-Hua Lian. "On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures." New Mathematics and Natural Computation 14, no. 03 (2018): 383–401. http://dx.doi.org/10.1142/s1793005718500230.

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Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-

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12

Rao, Ling, and Hongquan Chen. "Fictitious Domain Technique for the Calculation of Time-Periodic Solutions of Scattering Problem." Mathematical Problems in Engineering 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/503791.

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The fictitious domain technique is coupled to the improved time-explicit asymptotic method for calculating time-periodic solution of wave equation. Conventionally, the practical implementation of fictitious domain method relies on finite difference time discretizations schemes and finite element approximation. Our new method applies finite difference approximations in space instead of conventional finite element approximation. We use the Dirac delta function to transport the variational forms of the wave equations to the differential form and then solve it by finite difference schemes. Our met

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13

Almakadmeh, Khaled, and Alain Abran. "Experimental evaluation of an industrial technique for the approximation of software functional size." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 10, no. 3 (2013): 1459–74. http://dx.doi.org/10.24297/ijct.v10i3.3276.

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The Early & Quick sizing techniques, built based on ISO standards, have been proposed to derive an early approximation of software functional size when only high-level and incomplete requirements specifications are available. In the literature, there is a lack of research to evaluate the performance of such approximation sizing methods. This paper presents an experimental study to evaluate their reproducibility and accuracy. The experimental results show both poor reproducibility and large inaccurate approximations. In particular, the analysis of the findings indicates that the practitione

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14

Lamba, S., and B. Bandyopadhyay. "An improvement on Routh approximation technique." IEEE Transactions on Automatic Control 31, no. 11 (1986): 1047–50. http://dx.doi.org/10.1109/tac.1986.1104171.

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15

Tezduyar, Tayfun E., and Sunil Sathe. "Enhanced-approximation linear solution technique (EALST)." Computer Methods in Applied Mechanics and Engineering 193, no. 21-22 (2004): 2033–49. http://dx.doi.org/10.1016/j.cma.2003.12.045.

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16

NICOLA, AURELIAN, CONSTANTIN POPA, and ULRICH RUDE. "On a regularization technique for Kovarik-like approximate orthogonalization algorithms." Carpathian Journal of Mathematics 27, no. 1 (2011): 114–22. http://dx.doi.org/10.37193/cjm.2011.01.04.

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In this paper we consider four versions of Kovarik’s iterative orthogonalization algorithm, for approximating the minimal norm solution of symmetric least squares problems. Although the theoretical convergence rate of these algorithms is at least linear, in practical applications we observed that a too big number of iterations can dramatically deteriorate the already obtained approximation. In this respect we analyse the above mentioned Kovarik-like methods according to the modifications they make on the “machine zero” eigenvalues of the problem’s (symmetric) matrix. We establish a theoretical

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17

Zaidi, H. R. "Green's function equations of motion for driven two-level atoms." Canadian Journal of Physics 63, no. 3 (1985): 314–26. http://dx.doi.org/10.1139/p85-049.

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Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equatio

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18

Azam, Muhammad, Khalid Parvez, and Muhammad Omair. "Element-Free Galerkin Method Based on Block-Pulse Wavelets Integration for Solving Fourth-Order Obstacle Problem." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/308692.

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We introduce improved element-free Galerkin method based on block pulse wavelet integration for numerical approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. Moving least squares (MLS) approach is used to construct shape functions with optimized weight functions and basis. Numerical results for test problems are presented in this article to elaborate the pertinent features for the proposed technique. Comparison with existing techniques shows that our proposed method based on integration technique provide

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19

BELOMESTNY, DENIS, ANASTASIA KOLODKO, and JOHN SCHOENMAKERS. "PRICING CMS SPREAD OPTIONS IN A LIBOR MARKET MODEL." International Journal of Theoretical and Applied Finance 13, no. 01 (2010): 45–62. http://dx.doi.org/10.1142/s021902491000567x.

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We present two approximation methods for the pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.

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20

Menart, J. A., and HaeOk Skarda Lee. "Nongray Gas Analyses for Reflecting Walls Utilizing a Flux Technique." Journal of Heat Transfer 115, no. 3 (1993): 645–52. http://dx.doi.org/10.1115/1.2910735.

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A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a singl

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21

Redmann, Martin, and Peter Benner. "Singular perturbation approximation for linear systems with Lévy noise." Stochastics and Dynamics 18, no. 04 (2018): 1850033. http://dx.doi.org/10.1142/s0219493718500338.

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To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an e

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22

Luksch, Christian, Lukas Prost, and Michael Wimmer. "Real-time Approximation of Photometric Polygonal Lights." Proceedings of the ACM on Computer Graphics and Interactive Techniques 3, no. 1 (2020): 1–18. http://dx.doi.org/10.1145/3384537.

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We present a real-time rendering technique for photometric polygonal lights. Our method uses a numerical integration technique based on a triangulation to calculate noise-free diffuse shading. We include a dynamic point in the triangulation that provides a continuous near-field illumination resembling the shape of the light emitter and its characteristics. We evaluate the accuracy of our approach with a diverse selection of photometric measurement data sets in a comprehensive benchmark framework. Furthermore, we provide an extension for specular reflection on surfaces with arbitrary roughness

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23

Powar, P. L., Rishabh Tiwari, and Vishnu Narayan Mishra. "Extension of Dasgupta’s Technique for Higher Degree Approximation." Universitas Scientiarum 26, no. 2 (2021): 139–57. http://dx.doi.org/10.11144/javeriana.sc26-2.eodt.

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In the present paper, rational wedge functions for degree two approximation have been computed over a pentagonal discretization of the domain, by using an analytic approach which is an extension of Dasgupta’s approach for linear approximation. This technique allows to avoid the computation of the exterior intersection points of the elements, which was a key component of the technique initiated by Wachspress. The necessary condition for the existence of the denominator function was established by Wachspress whereas our assertion, induced by the technique of Dasgupta, assures the sufficiency of

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24

Park, Chang-Kyu. "Study on an Approximation Technique using MDO." Journal of the Korea Academia-Industrial cooperation Society 16, no. 6 (2015): 3661–66. http://dx.doi.org/10.5762/kais.2015.16.6.3661.

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25

Prahlow, Joseph A., and Patrick E. Lantz. "Cyanoacrylate Adhesive Technique in Wound Edge Approximation." Journal of Forensic Sciences 38, no. 6 (1993): 13559J. http://dx.doi.org/10.1520/jfs13559j.

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26

Fitzpatrick, Patrick, and John Flynn. "A Gröbner basis technique for Padé approximation." Journal of Symbolic Computation 13, no. 2 (1992): 133–38. http://dx.doi.org/10.1016/s0747-7171(08)80087-9.

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27

Gonzalez, J., H. Rojas, J. Ortega, and A. Prieto. "A new clustering technique for function approximation." IEEE Transactions on Neural Networks 13, no. 1 (2002): 132–42. http://dx.doi.org/10.1109/72.977289.

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28

Zielinski, Przemyslaw A. "An approximation technique for stochastic environmental modeling." Water Resources Research 29, no. 10 (1993): 3379–87. http://dx.doi.org/10.1029/93wr01167.

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Dianich, David F., and Jatinder N. D. Gupta. "Polynomial approximation technique for dynamic optimization problems." Computers & Operations Research 13, no. 4 (1986): 437–42. http://dx.doi.org/10.1016/0305-0548(86)90031-6.

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Hausken, Kjell, and John F. Moxnes. "A closure approximation technique for epidemic models." Mathematical and Computer Modelling of Dynamical Systems 16, no. 6 (2010): 555–74. http://dx.doi.org/10.1080/13873954.2010.496149.

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Saitoh, Satoru, Yukio Nakatsuchi, and Eiji Kitagawa. "Technique for bone approximation in ulna shortening." Journal of Hand Surgery 18, no. 5 (1993): 942. http://dx.doi.org/10.1016/0363-5023(93)90069-f.

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32

Diehl, Moritz, Hans Georg Bock, and Ekaterina Kostina. "An approximation technique for robust nonlinear optimization." Mathematical Programming 107, no. 1-2 (2005): 213–30. http://dx.doi.org/10.1007/s10107-005-0685-1.

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33

Deheuvels, P., D. Pfeifer, and Madan L. Puri. "A new semigroup technique in poisson approximation." Semigroup Forum 38, no. 1 (1989): 189–201. http://dx.doi.org/10.1007/bf02573230.

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Prahlow, J. A., and P. E. Lantz. "Cyanoacrylate adhesive technique in wound edge approximation." Journal of Clinical Forensic Medicine 1, no. 2 (1994): 116. http://dx.doi.org/10.1016/1353-1131(94)90019-1.

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35

Al-Saggaf, Ubaid M. "An approximation technique to tune PID controllers." Computers & Electrical Engineering 17, no. 4 (1991): 313–20. http://dx.doi.org/10.1016/0045-7906(91)90015-r.

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Clarke, Stella M., Jan H. Griebsch, and Timothy W. Simpson. "Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses." Journal of Mechanical Design 127, no. 6 (2004): 1077–87. http://dx.doi.org/10.1115/1.1897403.

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A variety of metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a “model of a model” to provide a fast surrogate for a computationally expensive computer code. Common metamodeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we investigate support vector regression (SVR) as an alternative technique for approximating complex engineering analyses. The computational

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Eck, Bradley J., and Martin Mevissen. "Quadratic approximations for pipe friction." Journal of Hydroinformatics 17, no. 3 (2014): 462–72. http://dx.doi.org/10.2166/hydro.2014.170.

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This paper develops quadratic approximations to the classical models of Darcy–Weisbach and Hazen–Williams for frictional head loss in water pipes. Key elements of the technique are selecting the approximation domain and minimizing the relative error. A comparison for individual pipes over a range of diameter, roughness, and Reynolds number showed that the approximation provides accuracy consistent with the experimental error in the classical equations. Two benchmark water distribution networks are also considered. In these systems, flows and pressures computed using the approximation were cons

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Girosi, Federico. "An Equivalence Between Sparse Approximation and Support Vector Machines." Neural Computation 10, no. 6 (1998): 1455–80. http://dx.doi.org/10.1162/089976698300017269.

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This article shows a relationship between two different approximation techniques: the support vector machines (SVM), proposed by V. Vapnik (1995) and a sparse approximation scheme that resembles the basis pursuit denoising algorithm (Chen, 1995; Chen, Donoho, & Saunders, 1995). SVM is a technique that can be derived from the structural risk minimization principle (Vapnik, 1982) and can be used to estimate the parameters of several different approximation schemes, including radial basis functions, algebraic and trigonometric polynomials, B-splines, and some forms of multilayer perceptrons.

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Imran, Muhammad, Abdul Ghafoor, and Victor Sreeram. "Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/498453.

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Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack o

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Sayyafzadeh, Mohammad, and Manouchehr Haghighi. "An assessment of different model-management techniques in history-matching problems for reservoir modelling." APPEA Journal 53, no. 1 (2013): 391. http://dx.doi.org/10.1071/aj12035.

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History matching is a computationally expensive inverse problem. The computation costs are dominantly associated with the optimisation step. Fitness approximation (proxy-modelling) approaches are common methods for reducing computational costs where the time-consuming original fitness function is substituted with an undemanding function known as approximation function (proxy). Almost all of the applied fitness approximation methods in history-matching problems use a similar approach called uncontrolled fitness approximation. It has been corroborated that the uncontrolled fitness approximation

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Feng, Hao, Rana Ashkar, Nina Steinke, et al. "Grating-based holographic diffraction methods for X-rays and neutrons: phase object approximation and dynamical theory." Journal of Applied Crystallography 51, no. 1 (2018): 68–75. http://dx.doi.org/10.1107/s1600576717016867.

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A method dubbed grating-based holography was recently used to determine the structure of colloidal fluids in the rectangular grooves of a diffraction grating from X-ray scattering measurements. Similar grating-based measurements have also been recently made with neutrons using a technique called spin-echo small-angle neutron scattering. The analysis of the X-ray diffraction data was done using an approximation that treats the X-ray phase change caused by the colloidal structure as a small perturbation to the overall phase pattern generated by the grating. In this paper, the adequacy of this we

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Halla, Martin. "Galerkin approximation of holomorphic eigenvalue problems: weak T-coercivity and T-compatibility." Numerische Mathematik 148, no. 2 (2021): 387–407. http://dx.doi.org/10.1007/s00211-021-01205-8.

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AbstractWe consider Galerkin approximations of eigenvalue problems for holomorphic Fredholm operator functions for which the operators do not have the structure “coercive+compact”. In this case the regularity (in the vocabulary of discrete approximation schemes) of Galerkin approximations is not unconditionally satisfied and the question of convergence is delicate. We report a technique to prove regularity of approximations which is applicable to a wide range of eigenvalue problems. The technique is based on the knowledge of a suitable Test function operator. In particular, we introduce the co

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PREDESCU, CRISTIAN. "SPATIALLY-DISCRETIZED HIGH-TEMPERATURE APPROXIMATIONS AND THEIR O(N) IMPLEMENTATION ON A GRID." Journal of Theoretical and Computational Chemistry 05, no. 02 (2006): 255–80. http://dx.doi.org/10.1142/s0219633606002246.

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We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N), with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter–Suzuki approximation again

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Big-Alabo, Akuro, Philip Harrison, and Matthew P. Cartmell. "Algorithm for the solution of elastoplastic half-space impact: Force-indentation linearisation method." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 5 (2014): 850–58. http://dx.doi.org/10.1177/0954406214541431.

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The governing equation of a half-space impact is generally nonlinear and it is normally solved using numerical techniques that are mostly conditionally stable and require many iteration steps for convergence of the solution. In this paper, we present the force-indentation linearisation method (FILM), an approximate technique that produces closed-form solutions of piecewise linearisation of the governing nonlinear differential equation and is capable of producing accurate impact response for an elastoplastic half-space impact. In contrast to the existing numerical techniques, which discretise t

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OPITZ, KARSTEN, and HELMUT POTTMANN. "COMPUTING SHORTEST PATHS ON POLYHEDRA: APPLICATIONS IN GEOMETRIC MODELING AND SCIENTIFIC VISUALIZATION." International Journal of Computational Geometry & Applications 04, no. 02 (1994): 165–78. http://dx.doi.org/10.1142/s0218195994000112.

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The application of shortest path calculations on polyhedra in different problem domains is discussed. A technique is introduced which allows to transfer problems defined on a curved domain surface into a plane. The technique is based on an approximation to the inverse exponential map. It is applied to gradient estimation for scattered data on surfaces and for the construction of local surface approximations from unorganized points.

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Zhang, Hua, Lu Yang Hou, and Guo Song Wei. "A Kriging Model-Based Approximation Technique for Predictive Design." Applied Mechanics and Materials 733 (February 2015): 871–75. http://dx.doi.org/10.4028/www.scientific.net/amm.733.871.

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Modern engineering optimization design technology often employs model building, analysis and computational optimization, which is computational expense and highly time cost, thus we need to employ approximation techniques to simplify the prototype model. We herein studied a Kriging Surrogate Model-based approximation technique, and employed it for predictive design. We firstly investigated the fit type: Anisotropic fit and Isotropic fit. And we compared two correlation functions: Gaussian and Marten Cubic. We also studied the effect of sample points on approximation accuracy. Then we built a K

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Ganji, S. S., M. G. Sfahani, S. M. Modares Tonekaboni, A. K. Moosavi, and D. D. Ganji. "Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method." Mathematical Problems in Engineering 2009 (2009): 1–20. http://dx.doi.org/10.1155/2009/327462.

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We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method (PEM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces tolerable error 3.14% as the maximum. By the second iteration the respective error became 1/5th, as it is 0.064%. So we conclude that the first approximation of PEM is so benefit when a quick answer is

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Biazar, Jafar, and Mohsen Didgar. "Numerical Solution of Riccati Equations by the Adomian and Asymptotic Decomposition Methods over Extended Domains." International Journal of Differential Equations 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/580741.

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We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation.

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Lieberman, Offer. "On the Approximation of Saddlepoint Expansions in Statistics." Econometric Theory 10, no. 5 (1994): 900–916. http://dx.doi.org/10.1017/s0266466600008914.

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The saddlepoint approximation as developed by Daniels [3] is an extremely accurate method for approximating probability distributions. Econometric and statistical applications of the technique to densities of statistics of interest are often hindered by the requirements of explicit knowledge of the c.g.f. and the need to obtain an analytical solution to the saddlepoint defining equation. In this paper, we show the conditions under which any approximation to the saddlepoint is justified and suggest a convenient solution. We illustrate with an approximate saddlepoint expansion of the Durbin-Wats

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Parsa, Z., and V. Zadorozhny. "Approximation technique for solving the Vlasov–Poisson problem." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 558, no. 1 (2006): 311–13. http://dx.doi.org/10.1016/j.nima.2005.11.030.

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