Relevant bibliographies by topics / Numerical approximation algorithms

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Numerical approximation algorithms'

Author: Grafiati
Published: 5 June 2025
Last updated: 2 August 2025

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Journal articles on the topic "Numerical approximation algorithms"

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Jafari, Reza. "Stability Analysis of Recurrent-Neural-Based Controllers Using Dissipativity Domain." Mathematics 11, no. 14 (2023): 3050. http://dx.doi.org/10.3390/math11143050.

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This paper proposes a method for the stability analysis of dynamic neural networks. The stability analysis of dynamic neural networks is a challenging task due to internal feedback connections. In this research work, we propose an algorithm based on the Reduction of Dissipativity Domain (RODD) algorithm. The RODD algorithm is a numerical technique for the detection of the stability of nonlinear dynamic systems. The method works by using an approximation of the reachable set. This paper proposes linear and quadratic approximations of reachable sets. RODD-LB uses a linear approximation, RODD-EB
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Ding, Shuo, Xiao Heng Chang, and Qing Hui Wu. "A Study on Approximation Performances of Improved Bp Neural Networks Based on LM Algorithms." Applied Mechanics and Materials 411-414 (September 2013): 1935–38. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1935.

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When approximating nonlinear functions, standard BP algorithms and traditional improved BP algorithms have low convergence rate and tend to be stuck in local minimums. In this paper, standard BP algorithm is improved by numerical optimization algorithm. Firstly, the principle of Levenberg-Marquardt algorithm is introduced. Secondly, to test its approximation performance, LMBP neural network is programmed via MATLAB7.0 taking specific nonlinear function as an example. Thirdly, its approximation result is compared with those of standard BP algorithm and adaptive learning rate algorithm. Simulati
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DeVore, Ronald, Boris Hanin, and Guergana Petrova. "Neural network approximation." Acta Numerica 30 (May 2021): 327–444. http://dx.doi.org/10.1017/s0962492921000052.

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Neural networks (NNs) are the method of choice for building learning algorithms. They are now being investigated for other numerical tasks such as solving high-dimensional partial differential equations. Their popularity stems from their empirical success on several challenging learning problems (computer chess/Go, autonomous navigation, face recognition). However, most scholars agree that a convincing theoretical explanation for this success is still lacking. Since these applications revolve around approximating an unknown function from data observations, part of the answer must involve the a
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Duan, Beiping, Raytcho D. Lazarov, and Joseph E. Pasciak. "Numerical approximation of fractional powers of elliptic operators." IMA Journal of Numerical Analysis 40, no. 3 (2019): 1746–71. http://dx.doi.org/10.1093/imanum/drz013.

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Abstract In this paper, we develop and study algorithms for approximately solving linear algebraic systems: ${{\mathcal{A}}}_h^\alpha u_h = f_h$, $ 0< \alpha <1$, for $u_h, f_h \in V_h$ with $V_h$ a finite element approximation space. Such problems arise in finite element or finite difference approximations of the problem $ {{\mathcal{A}}}^\alpha u=f$ with ${{\mathcal{A}}}$, for example, coming from a second-order elliptic operator with homogeneous boundary conditions. The algorithms are motivated by the method of Vabishchevich (2015, Numerically solving an equation for fractiona
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Martinsson, Per-Gunnar, and Joel A. Tropp. "Randomized numerical linear algebra: Foundations and algorithms." Acta Numerica 29 (May 2020): 403–572. http://dx.doi.org/10.1017/s0962492920000021.

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This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues.Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nyst
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Guo, Yuanzhen, Hao Xiong, and Nicholas Ruozzi. "Marginal Inference in Continuous Markov Random Fields Using Mixtures." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7834–41. http://dx.doi.org/10.1609/aaai.v33i01.33017834.

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Exact marginal inference in continuous graphical models is computationally challenging outside of a few special cases. Existing work on approximate inference has focused on approximately computing the messages as part of the loopy belief propagation algorithm either via sampling methods or moment matching relaxations. In this work, we present an alternative family of approximations that, instead of approximating the messages, approximates the beliefs in the continuous Bethe free energy using mixture distributions. We show that these types of approximations can be combined with numerical quadra
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Chang, Qianshun, and Rong-Qing Jia. "A refined convergence analysis of multigrid algorithms for elliptic equations." Analysis and Applications 13, no. 03 (2015): 255–90. http://dx.doi.org/10.1142/s0219530514500080.

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Multigrid algorithms, in particular, multigrid V-cycles, are investigated in this paper. We establish a general theory for convergence of the multigrid algorithm under certain approximation conditions and smoothing conditions. Our smoothing conditions are satisfied by commonly used smoothing operators including the standard Gauss–Seidel method. Our approximation conditions are verified for finite element approximation to numerical solutions of elliptic partial differential equations without any requirement of additional regularity of the solution. Our convergence analysis of multigrid algorith
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Cohen, Albert, and Ronald DeVore. "Approximation of high-dimensional parametric PDEs." Acta Numerica 24 (April 27, 2015): 1–159. http://dx.doi.org/10.1017/s0962492915000033.

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Parametrized families of PDEs arise in various contexts such as inverse problems, control and optimization, risk assessment, and uncertainty quantification. In most of these applications, the number of parameters is large or perhaps even infinite. Thus, the development of numerical methods for these parametric problems is faced with the possible curse of dimensionality. This article is directed at (i) identifying and understanding which properties of parametric equations allow one to avoid this curse and (ii) developing and analysing effective numerical methods which fully exploit these proper
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Temlyakov, V. N. "Greedy approximation." Acta Numerica 17 (April 25, 2008): 235–409. http://dx.doi.org/10.1017/s0962492906380014.

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In this survey we discuss properties of specific methods of approximation that belong to a family of greedy approximation methods (greedy algorithms). It is now well understood that we need to study nonlinear sparse representations in order to significantly increase our ability to process (compress, denoise,etc.) large data sets. Sparse representations of a function are not only a powerful analytic tool but they are utilized in many application areas such as image/signal processing and numerical computation. The key to finding sparse representations is the concept ofm-term approximation of the
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L, Hart, and Yatsechko N. "Numerical algorithms for solving an elliptic optimal control problem with a power-law nonlinearity." Artificial Intelligence 26, jai2021.26(2) (2021): 64–76. http://dx.doi.org/10.15407/jai2021.02.064.

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The paper is devoted to the development and analysis of approximation-iteration algorithms based on the method of grids and the method of lines for solving an elliptic optimal control problem with a power-law nonlinearity. For the numerical solution of the main boundary value problem and the adjoint one, the second order of accuracy difference schemes are applied using the implicit method of simple iteration. Computational schemes of the method of lines for solving the above-mentioned elliptic boundary value problems are implemented in combination with the shooting method for the approximate s
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Dissertations / Theses on the topic "Numerical approximation algorithms"

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Javed, Mohsin. "Algorithms for trigonometric polynomial and rational approximation." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:23a36d72-0299-4c63-98e8-d0aa088c062e.

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This thesis presents new numerical algorithms for approximating functions by trigonometric polynomials and trigonometric rational functions. We begin by reviewing trigonometric polynomial interpolation and the barycentric formula for trigonometric polynomial interpolation in Chapter 1. Another feature of this chapter is the use of the complex plane, contour integrals and phase portraits for visualising various properties and relationships between periodic functions and their Laurent and trigonometric series. We also derive a periodic analogue of the Hermite integral formula which enables us to
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Pachon, Ricardo. "Algorithms for polynomial and rational approximation." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:f268a835-46ef-45ea-8610-77bf654b9442.

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Robust algorithms for the approximation of functions are studied and developed in this thesis. Novel results and algorithms on piecewise polynomial interpolation, rational interpolation and best polynomial and rational approximations are presented. Algorithms for the extension of Chebfun, a software system for the numerical computation with functions, are described. These algorithms allow the construction and manipulation of piecewise smooth functions numerically with machine precision. Breakpoints delimiting subintervals are introduced explicitly, implicitly or automatically, the latter metho
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Valenzuela, Zaldy M. "Constant and power-of-2 segmentation algorithms for a high speed numerical function generator." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Jun%5FValenzuela.pdf.

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Mishchenko, Kateryna. "Numerical Algorithms for Optimization Problems in Genetical Analysis." Doctoral thesis, Västerås : Scool of education, Culture and Communication, Mälardalen University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-650.

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Platte, Rodrigo B. "Accuracy and stability of global radial basis function methods for the numerical solution of partial differential equations." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file 8.72Mb, 143 p, 2005. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3181853.

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Tung, Michael Ming-Sha. "Spline approximations for systems of ordinary differential equations." Doctoral thesis, Universitat Politècnica de València, 2013. http://hdl.handle.net/10251/31658.

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El objetivo de esta tesis doctoral es desarrollar nuevos métodos basados en splines para la resolución de sistemas de ecuaciones diferenciales del tipo Y'(x)=f(x,Y(x)) , a<x<b Y(a)=Y_a (1) donde Y_a, Y(x) son matrices rxq, comenzando con splines de tipo cúbico y con un algoritmo similar al propuesto por Loscalzo y Talbot en el caso escalar [20], intentando poder aumentar el orden del spline, lo que con el método dado en [20] no puede hacerse de forma convergente. Trataremos también de aplicar dicho método al problema Y''(x)=f(x,Y(x),Y'(x)) , a<x<b Y(a)=Y_a Y'(a)=Y_b
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Silva, Nunes Ana Luisa. "Spectral approximation with matrices issued from discretized operators." Phd thesis, Université Jean Monnet - Saint-Etienne, 2012. http://tel.archives-ouvertes.fr/tel-00952977.

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In this thesis, we consider the numerical solution of a large eigenvalue problem in which the integral operator comes from a radiative transfer problem. It is considered the use of hierarchical matrices, an efficient data-sparse representation of matrices, especially useful for large dimensional problems. It consists on low-rank subblocks leading to low memory requirements as well as cheap computational costs. We discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. T
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Whitinger, Robert. "An Algorithm for the Machine Calculation of Minimal Paths." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/3119.

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Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.
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Savas, Berkant. "Algorithms in data mining using matrix and tensor methods." Doctoral thesis, Linköpings universitet, Beräkningsvetenskap, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11597.

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In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem,
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Nguyen, Hung The. "Big Networks: Analysis and Optimal Control." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5514.

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The study of networks has seen a tremendous breed of researches due to the explosive spectrum of practical problems that involve networks as the access point. Those problems widely range from detecting functionally correlated proteins in biology to finding people to give discounts and gain maximum popularity of a product in economics. Thus, understanding and further being able to manipulate/control the development and evolution of the networks become critical tasks for network scientists. Despite the vast research effort putting towards these studies, the present state-of-the-arts largely eith
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Books on the topic "Numerical approximation algorithms"

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Ervedoza, Sylvain. Numerical Approximation of Exact Controls for Waves. Springer New York, 2013.

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Armin, Iske, Levesley Jeremy 1964-, and SpringerLink (Online service), eds. Approximation Algorithms for Complex Systems: Proceedings of the 6th International Conference on Algorithms for Approximation, Ambleside, UK, 31st August - 4th September 2009. Springer-Verlag Berlin Heidelberg, 2011.

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Gunzburger, Max D. On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations. National Aeronautics and Space Administration, 1986.

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1953-, Valli A. (Alberto), ed. Eddy current approximation of Maxwell Equations: Theory, algorithms and applications. Springer, 2010.

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Diskin, Boris. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Center, Langley Research, ed. Solving upwind-biased discretizations II: Multigrid solver using semicoarsening. National Aeronautics and Space Administration, Langley Research Center, 1999.

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Max-Planck-Institut. Combinatorics and physics: Mini-Workshop on Renormalization, December 15-16, 2006, Max Planck Institut für Mathematik, Bonn, Germany : Conference on Combinatorics and Physics, March 19-23, 2007, Max Planck Institut für Mathematik, Bonn, Germany. Edited by Ebrahimi-Fard Kurusch 1973-, Marcolli Matilde, Suijlekom, Walter D. van., 1978-, Max-Planck-Institut für Mathematik, and Conference on Combinatorics and Physics (2007 : Max Planck Institut für Mathematik). American Mathematical Society, 2011.

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International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (3rd 2000 Saarbrücken, Germany). Approximation algorithms for combinatorial optimization: Third international workshop, APPROX 2000, Saarbrucken, Germany, September 5-8, 2000 : proceedings. Springer, 2000.

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Book chapters on the topic "Numerical approximation algorithms"

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Engeln-Müllges, Gisela, and Frank Uhlig. "Linear and Nonlinear Approximation." In Numerical Algorithms with C. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61074-5_8.

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Engeln-Müllges, Gisela, and Frank Uhlig. "Linear and Nonlinear Approximation." In Numerical Algorithms with Fortran. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-80043-6_8.

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Trefethen, L. N. "Approximation theory and numerical linear algebra." In Algorithms for Approximation II. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_30.

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Saha Ray, Santanu. "Approximation of Functions." In Numerical Analysis with Algorithms and Programming. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315369174-9.

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Watson, G. A. "Numerical methods for Chebyshev approximation of complex-valued functions." In Algorithms for Approximation II. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_23.

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Iske, Armin. "Basic Methods and Numerical Algorithms." In Approximation Theory and Algorithms for Data Analysis. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-05228-7_2.

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Meyling, R. H. J. Gmelig. "Numerical solution of the biharmonic equation using different types of bivariate spline functions." In Algorithms for Approximation II. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_32.

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Walz, G. "Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation." In Algorithms for Approximation II. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_34.

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Levesley, Jeremy, Alexander N. Gorban, and David Packwood. "A Numerical Analyst’s View of the Lattice Boltzmann Method." In Approximation Algorithms for Complex Systems. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16876-5_6.

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Schaback, R. "Convergence Theorems for Nonlinear Approximation Algorithms." In Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie. Birkhäuser Basel, 1987. http://dx.doi.org/10.1007/978-3-0348-6656-9_17.

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Conference papers on the topic "Numerical approximation algorithms"

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Segeth, Karel. "Data approximation using polyharmonic radial basis functions." In Programs and Algorithms of Numerical Mathematics 20. Institute of Mathematics, Czech Academy of Sciences, 2021. http://dx.doi.org/10.21136/panm.2020.13.

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Gillard, Jonathan, Dmitri Kvasov, and Anatoly Zhigljavsky. "Optimization problems in structured low rank approximation." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965338.

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Segeth, Karel. "Spherical basis function approximation with particular trend functions." In Programs and Algorithms of Numerical Mathematics 21. Institute of Mathematics, Czech Academy of Sciences, 2023. http://dx.doi.org/10.21136/panm.2022.20.

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The paper is concerned with the measurement of scalar physical quantities at nodes on the $(d-1)$-dimensional unit sphere surface in the \hbox{$d$-dimensional} Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider $d=3$. We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful in the interpretation of many physical measurements. We show an example conce
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de Souza, Gilcélia Regiâne, and Jorge Stolfi. "General algorithms for multiscale approximation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992755.

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Plotnikov, Roman, Adil Erzin, and Nenad Mladenovic. "Approximation algorithms for the min-power symmetric connectivity problem." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965333.

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Serafini, Giada. "Numerical approximation of weakly singular integrals on a triangle." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965357.

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Valášek, Jan, Petr Sváček, and Jaromír Horáček. "On finite element approximation of flow induced vibration of elastic structure." In Programs and Algorithms of Numerical Mathematics 18. Institute of Mathematics, Czech Academy of Sciences, 2017. http://dx.doi.org/10.21136/panm.2016.17.

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Marhan, Tomáš, and Petr Sváček. "Numerical approximation of aeroacoustics induced by flow over a square cylinder." In Programs and Algorithms of Numerical Mathematics 22. Institute of Mathematics, Czech Academy of Sciences, 2025. https://doi.org/10.21136/panm.2024.11.

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Erzin, Adil I., and Yury A. Kochetov. "Preface to the special session Intractable problems and approximation algorithms." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965322.

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Russo, Maria Grazia, and Alessandra De Rossi. "Preface to the special session Approximation theory and its applications." In NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS (NUMTA–2016): Proceedings of the 2nd International Conference “Numerical Computations: Theory and Algorithms”. Author(s), 2016. http://dx.doi.org/10.1063/1.4965347.

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Reports on the topic "Numerical approximation algorithms"

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Eslami, Keyvan, and Thomas M. Phelan. The Art of Temporal Approximation: An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics. Federal Reserve Bank of Cleveland, 2023. http://dx.doi.org/10.26509/frbc-wp-202310.

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A recent literature within quantitative macroeconomics has advocated the use of continuous-time methods for dynamic programming problems. In this paper we explore the relative merits of continuous-time and discrete-time methods within the context of stationary and nonstationary income fluctuation problems. For stationary problems in two dimensions, the continuous-time approach is both more stable and typically faster than the discrete-time approach for any given level of accuracy. In contrast, for convex lifecycle problems (in which age or time enters explicitly), simply iterating backwards fr
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SECOND-ORDER ANALYSIS OF BEAM-COLUMNS BY MACHINE LEARNING-BASED STRUCTURAL ANALYSIS THROUGH PHYSICS-INFORMED NEURAL NETWORKS. The Hong Kong Institute of Steel Construction, 2023. http://dx.doi.org/10.18057/ijasc.2023.19.4.10.

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The second-order analysis of slender steel members could be challenging, especially when large deflection is involved. This paper proposes a novel machine learning-based structural analysis (MLSA) method for second-order analysis of beam-columns, which could be a promising alternative to the prevailing solutions using over-simplified analytical equations or traditional finite-element-based methods. The effectiveness of the conventional machine learning method heavily depends on both the qualitative and the quantitative of the provided data. However, such data are typically scarce and expensive
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