New Sinc Methods Of Numerical Analysis

Author : Gerd Baumann
Publisher : Springer Nature
ISBN 13 : 303049716X
Total Pages : 411 pages
Book Rating : 4.63/5 ( download)

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Download or read book New Sinc Methods of Numerical Analysis written by Gerd Baumann and published by Springer Nature. This book was released on 2021-04-23 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Author : Frank Stenger
Publisher : CRC Press
ISBN 13 : 9781138116177
Total Pages : 482 pages
Book Rating : 4.73/5 ( download)

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Download or read book Handbook of Sinc Numerical Methods written by Frank Stenger and published by CRC Press. This book was released on 2017-05-31 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author�s advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to scientists and engineers. This new theory, which combines Sinc convolution with the boundary integral equation (IE) approach, makes for exponentially faster convergence to solutions of differential equations. The basis for the approach is the Sinc method of approximating almost every type of operation stemming from calculus via easily computed matrices of very low dimension. The CD-ROM of this handbook contains roughly 450 MATLAB� programs corresponding to exponentially convergent numerical algorithms for solving nearly every computational problem of science and engineering. While the book makes Sinc methods accessible to users wanting to bypass the complete theory, it also offers sufficient theoretical details for readers who do want a full working understanding of this exciting area of numerical analysis.

Author : Frank Stenger
Publisher : CRC Press
ISBN 13 : 1439821593
Total Pages : 482 pages
Book Rating : 4.96/5 ( download)

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Download or read book Handbook of Sinc Numerical Methods written by Frank Stenger and published by CRC Press. This book was released on 2016-04-19 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Sinc Numerical Methods presents an ideal road map for handling general numeric problems. Reflecting the author's advances with Sinc since 1995, the text most notably provides a detailed exposition of the Sinc separation of variables method for numerically solving the full range of partial differential equations (PDEs) of interest to sci

Author : Frank Stenger
Publisher : Springer Science & Business Media
ISBN 13 : 1461227062
Total Pages : 580 pages
Book Rating : 4.69/5 ( download)

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Download or read book Numerical Methods Based on Sinc and Analytic Functions written by Frank Stenger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.

Author : John Lund
Publisher : SIAM
ISBN 13 : 9781611971637
Total Pages : 307 pages
Book Rating : 4.32/5 ( download)

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Download or read book Sinc Methods for Quadrature and Differential Equations written by John Lund and published by SIAM. This book was released on 1992-01-01 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations. These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions. The text is written to facilitate easy implementation of the theory into operating numerical code. The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method. Many of these applications are useful in numerical processes of interest quite independent of differential equations. Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right. The intimate connection between collocation and Galerkin for the sinc basis is exposed via sinc-interpolation. The quadrature rules define a class of numerical integration methods that complement better known techniques, which in the case of singular integrands, often require modification. The sinc methodology of the text is illustrated on such applications as initial data recovery, heat diffusion, advective-diffusive transport, and Burgers' equation, to illustrate the numerical implementation of the theory discussed. Engineers may find sinc methods a very competitive approach to the more common boundary element or finite element methods. Further, workers in the signal processing community may find this particular approach a refreshingly different view of the use of sinc functions. Sinc approximation is a relatively new numerical technique. This book provides a much needed elementary level explanation. It has been used for graduate numerical classes at Montana State University and Texas Tech University.

Author : A. Cohen
Publisher : Elsevier
ISBN 13 : 0080537855
Total Pages : 357 pages
Book Rating : 4.56/5 ( download)

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Download or read book Numerical Analysis of Wavelet Methods written by A. Cohen and published by Elsevier. This book was released on 2003-04-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

Author : David Gottlieb
Publisher : SIAM
ISBN 13 : 0898710235
Total Pages : 167 pages
Book Rating : 4.36/5 ( download)

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Download or read book Numerical Analysis of Spectral Methods written by David Gottlieb and published by SIAM. This book was released on 1977-01-01 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.

Author : James P Howard, II
Publisher : CRC Press
ISBN 13 : 1498723640
Total Pages : 257 pages
Book Rating : 4.40/5 ( download)

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Download or read book Computational Methods for Numerical Analysis with R written by James P Howard, II and published by CRC Press. This book was released on 2017-07-12 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Author : Adhemar Bultheel
Publisher : World Scientific
ISBN 13 : 9812836268
Total Pages : 240 pages
Book Rating : 4.67/5 ( download)

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Download or read book The Birth of Numerical Analysis written by Adhemar Bultheel and published by World Scientific. This book was released on 2010 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Author : Larkin Ridgway Scott
Publisher : Princeton University Press
ISBN 13 : 1400838967
Total Pages : 342 pages
Book Rating : 4.67/5 ( download)

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Download or read book Numerical Analysis written by Larkin Ridgway Scott and published by Princeton University Press. This book was released on 2011-04-18 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin