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Relevant bibliographies by topics / Approximations and expansions – Approximations and expansions – Approximation by rational functions

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Academic literature on the topic 'Approximations and expansions – Approximations and expansions – Approximation by rational functions'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Approximations and expansions – Approximations and expansions – Approximation by rational functions"

1

Telste, J. G., and F. Noblesse. "Numerical Evaluation of the Green Function of Water-Wave Radiation and Diffraction." Journal of Ship Research 30, no. 02 (1986): 69–84. http://dx.doi.org/10.5957/jsr.1986.30.2.69.

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This study presents a simple, accurate, and efficient method for numerically evaluating the Green function, and its gradient, of the theory of water-wave radiation and diffraction. The method is based on five expressions for the Green function that are useful in complementary regions of the quadrant in which the Green function is defined. These expressions consist of asymptotic expansions, ascending series, two complementary Taylor series, and a numerical approximation based on a modified form of the Haskind integral representation. The four series representations are refinements of the series

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2

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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3

YILMAZ, ÖZGÜR. "ON COARSE QUANTIZATION OF TIGHT GABOR FRAME EXPANSIONS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 02 (2005): 283–99. http://dx.doi.org/10.1142/s0219691305000853.

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This paper presents a coarse quantization algorithm (TFΣΔ-II) for tight Gabor frame expansions of certain functions in L2(ℝ), an alternative to the TFΣΔ of Ref. 11. By using some a priori information about the function to be quantized and compromising the translation invariance of the TFΣΔ, TFΣΔ-II produces an approximation in L2(ℝ), as opposed to the weak type approximations of TFΣΔ. In particular, for a tight Gabor frame with frame bound A, we prove that the L2-approximation error corresponding to a kth-order TFΣΔ-II quantizer is of order O(A-k). Furthermore, motivated by TFΣΔ-II, we constru

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4

Martin, Pablo, Eduardo Rojas, Jorge Olivares, and Adrián Sotomayor. "Quasi-Rational Analytic Approximation for the Modified Bessel Function I1(x) with High Accuracy." Symmetry 13, no. 5 (2021): 741. http://dx.doi.org/10.3390/sym13050741.

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A new simple and accurate expression to approximate the modified Bessel function of the first kind I1(x) is presented in this work. This new approximation is obtained as an improvement of the multi-point quasi-rational approximation technique, MPQA. This method uses the power series of the Bessel function, its asymptotic expansion, and a process of optimization to fit the parameters of a fitting function. The fitting expression is formed by elementary functions combined with rational ones. In the present work, a sum of hyperbolic functions was selected as elementary functions to capture the fi

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5

Pizio, O. A., and Z. B. Halytch. "Structural Properties of the Ion-Dipole Model of Electrolyte Solutions in the Bulk and Near a Charged Hard Wall.Application of the Truncated Optimized Cluster Series." Zeitschrift für Naturforschung A 46, no. 1-2 (1991): 8–18. http://dx.doi.org/10.1515/zna-1991-1-203.

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AbstractAn ion-dipole model of electrolyte solutions in the bulk case and near a charged or uncharged hard wall is considered. A method to derive the terms of optimized cluster expansions for the distribution functions of ions and dipoles which provides a set of approximations beyond the mean spherical approximation is given. The third cluster coefficient approximation is investigated

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6

Fischler, S., and T. Rivoal. "Rational approximation to values of G-functions, and their expansions in integer bases." manuscripta mathematica 155, no. 3-4 (2017): 579–95. http://dx.doi.org/10.1007/s00229-017-0933-8.

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7

Zhang, Zhihua. "Fourier Expansions with Polynomial Terms for Random Processes." Journal of Function Spaces 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/763075.

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Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also n

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8

Angulo, J. M., and M. D. Ruiz-Medina. "Multi-resolution approximation to the stochastic inverse problem." Advances in Applied Probability 31, no. 04 (1999): 1039–57. http://dx.doi.org/10.1017/s0001867800009617.

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The linear inverse problem of estimating the input random field in a first-kind stochastic integral equation relating two random fields is considered. For a wide class of integral operators, which includes the positive rational functions of a self-adjoint elliptic differential operator on L 2(ℝ d ), the ill-posed nature of the problem disappears when such operators are defined between appropriate fractional Sobolev spaces. In this paper, we exploit this fact to reconstruct the input random field from the orthogonal expansion (i.e. with uncorrelated coefficients) derived for the output random f

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9

Angulo, J. M., and M. D. Ruiz-Medina. "Multi-resolution approximation to the stochastic inverse problem." Advances in Applied Probability 31, no. 4 (1999): 1039–57. http://dx.doi.org/10.1239/aap/1029955259.

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The linear inverse problem of estimating the input random field in a first-kind stochastic integral equation relating two random fields is considered. For a wide class of integral operators, which includes the positive rational functions of a self-adjoint elliptic differential operator on L2(ℝd), the ill-posed nature of the problem disappears when such operators are defined between appropriate fractional Sobolev spaces. In this paper, we exploit this fact to reconstruct the input random field from the orthogonal expansion (i.e. with uncorrelated coefficients) derived for the output random fiel

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10

Kops, J. Christopher. "Selmer's Multiplicative Algorithm." Integers 12, no. 1 (2012): 1–20. http://dx.doi.org/10.1515/integ.2011.080.

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Abstract.The behavior of the multiplicative acceleration of Selmer's algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.

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Dissertations / Theses on the topic "Approximations and expansions – Approximations and expansions – Approximation by rational functions"

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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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Books on the topic "Approximations and expansions – Approximations and expansions – Approximation by rational functions"

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1968-, Arvesú Jorge, and Lopez Lagomasino Guillermo 1948-, eds. Recent advances in orthogonal polynomials, special functions, and their applications: 11th International Symposium on Orthogonal Polynomials, Special Functions, and Their Applications, August 29-September 2, 2011, Universidad Carlos III de Madrid, Leganes, Spain. American Mathematical Society, 2012.

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Dai, Feng. Approximation Theory and Harmonic Analysis on Spheres and Balls. Springer New York, 2013.

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3

Saff, E. B., Douglas Patten Hardin, Brian Z. Simanek, and D. S. Lubinsky. Modern trends in constructive function theory: Conference in honor of Ed Saff's 70th birthday : constructive functions 2014, May 26-30, 2014, Vanderbilt University, Nashville, Tennessee. American Mathematical Society, 2016.

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4

Michel, Volker. Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball. Birkhäuser Boston, 2013.

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Allen, Zalcman Lawrence, ed. Complex proofs of real theorems. American Mathematical Society, 2012.

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6

Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic

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7

Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic

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Book chapters on the topic "Approximations and expansions – Approximations and expansions – Approximation by rational functions"

1

Andrianov, Igor, and Anatoly Shatrov. "Padé Approximation to Solve the Problems of Aerodynamics and Heat Transfer in the Boundary Layer." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.93084.

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In this chapter, we describe the applications of asymptotic methods to the problems of mathematical physics and mechanics, primarily, to the solution of nonlinear singular perturbed problems. We also discuss the applications of Padé approximations for the transformation of asymptotic expansions to rational or quasi-fractional functions. The applications of the method of matching of internal and external asymptotics in the problem of boundary layer of viscous gas by means of Padé approximation are considered.

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