Numerical Methods Iii Approximation Of Functions
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Approximation Of Functions Theory And Numerical Methods
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Author : Günter Meinardus
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximation Of Functions Theory And Numerical Methods written by Günter Meinardus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
for example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J. L. WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COLLATZ for his many encouragements for the writing of this book. Thanks are equally due to Springer-Verlag for their ready agreement to my wishes, and for the excellent and competent composition of the book. In addition, I would like to thank Dr. W. KRABS, Dr. A. -G. MEYER and D. SCHWEDT for their very careful reading of the manuscript. Hamburg, March 1964 GUNTER MEINARDUS Preface to the English Edition This English edition was translated by Dr. LARRY SCHUMAKER, Mathematics Research Center, United States Army, The University of Wisconsin, Madison, from a supplemented version of the German edition. Apart from a number of minor additions and corrections and a few new proofs (e. g. , the new proof of JACKSON'S Theorem), it differs in detail from the first edition by the inclusion of a discussion of new work on comparison theorems in the case of so-called regular Haar systems (§ 6) and on Segment Approximation (§ 11). I want to thank the many readers who provided comments and helpful suggestions. My special thanks are due to the translator, to Springer-Verlag for their ready compliance with all my wishes, to Mr.
Numerical Approximation Methods
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Author : Harold Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-28
Numerical Approximation Methods written by Harold Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.
This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Approximation Of Functions Theory And Numerical Methods
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Author : Günter Meinardus
language : en
Publisher:
Release Date : 1967
Approximation Of Functions Theory And Numerical Methods written by Günter Meinardus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Approximation theory categories.
Approximation Theory And Numerical Methods
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Author : G. A. Watson
language : en
Publisher: John Wiley & Sons
Release Date : 1980
Approximation Theory And Numerical Methods written by G. A. Watson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
An Introduction To Numerical Methods
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Author : Abdelwahab Kharab
language : en
Publisher: CRC Press
Release Date : 2011-11-16
An Introduction To Numerical Methods written by Abdelwahab Kharab and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-16 with Mathematics categories.
Highly recommended by CHOICE, previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Third Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computer results so that the main steps are easily visualized and interpreted. New to the Third Edition A chapter on the numerical solution of integral equations A section on nonlinear partial differential equations (PDEs) in the last chapter Inclusion of MATLAB GUIs throughout the text The book begins with simple theoretical and computational topics, including computer floating point arithmetic, errors, interval arithmetic, and the root of equations. After presenting direct and iterative methods for solving systems of linear equations, the authors discuss interpolation, spline functions, concepts of least-squares data fitting, and numerical optimization. They then focus on numerical differentiation and efficient integration techniques as well as a variety of numerical techniques for solving linear integral equations, ordinary differential equations, and boundary-value problems. The book concludes with numerical techniques for computing the eigenvalues and eigenvectors of a matrix and for solving PDEs. CD-ROM Resource The accompanying CD-ROM contains simple MATLAB functions that help students understand how the methods work. These functions provide a clear, step-by-step explanation of the mechanism behind the algorithm of each numerical method and guide students through the calculations necessary to understand the algorithm. Written in an easy-to-follow, simple style, this text improves students’ ability to master the theoretical and practical elements of the methods. Through this book, they will be able to solve many numerical problems using MATLAB.
Weighted Polynomial Approximation And Numerical Methods For Integral Equations
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Author : Peter Junghanns
language : en
Publisher: Springer Nature
Release Date : 2021-08-10
Weighted Polynomial Approximation And Numerical Methods For Integral Equations written by Peter Junghanns and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Mathematics categories.
The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
Numerical Methods For Special Functions
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Author : Amparo Gil
language : en
Publisher: SIAM
Release Date : 2007-01-01
Numerical Methods For Special Functions written by Amparo Gil and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).
Numerical Analysis
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Author : Vinay Vachharajani
language : en
Publisher: BPB Publications
Release Date : 2018-06-01
Numerical Analysis written by Vinay Vachharajani and has been published by BPB Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-01 with Computers categories.
Description:This book is Designed to serve as a text book for the undergraduate as well as post graduate students of Mathematics, Engineering, Computer Science.COVERAGE:Concept of numbers and their accuracy, binary and decimal number system, limitations of floating point representation.Concept of error and their types, propagation of errors through process graph.Iterative methods for finding the roots of algebraic and transcendental equations with their convergence, methods to solve the set of non-linear equations, methods to obtain complex roots.Concept of matrices, the direct and iterative methods to solve a system of linear algebraic equations.Finite differences, interpolation and extrapolation methods, cubic spline, concept of curve fitting.Differentiation and integration methods.Solution of ordinary and partial differential equations SALIENT FEATURES:Chapters include objectives, learning outcomes, multiple choice questions, exercises for practice and solutions.Programs are written in C Language for Numerical methods.Topics are explained with suitable examples.Arrangement (Logical order), clarity, detailed presentation and explanation of each topic with numerous solved and unsolved examples.Concise but lucid and student friendly presentation for derivation of formulas used in various numerical methods. Table Of Contents:Computer ArithmeticError Analysis Solution of Algebraic and Transcendental Equations Solution of System of Linear Equations and Eigen value Problems Finite Differences Interpolation Curve Fitting and Approximation Numerical Differentiation Numerical Integration Difference Equations Numerical Solution of Ordinary Differential Equations Numerical Solution of Partial Differential Equations Appendix - I Case Studies / Applications Appendix - II Synthetic Division Bibliography Index
Numerical Methods In Software And Analysis
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Author : John R. Rice
language : en
Publisher: Elsevier
Release Date : 2014-05-19
Numerical Methods In Software And Analysis written by John R. Rice and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Mathematics categories.
Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem—there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithms. The book is organized into three parts. Part I presents the background material. Part II presents the principal methods and ideas of numerical computation. Part III contains material about software engineering and performance evaluation. A uniform approach is used in each area of numerical computation. First, an intuitive development is made of the problems and the basic methods for their solution. Then, relevant mathematical software is reviewed and its use outlined. Many areas provide extensive examples and case studies. Finally, a deeper analysis of the methods is presented as in traditional numerical analysis texts. Emphasizes the use of high-quality mathematical software for numerical computation Extensive use of IMSL routines Features extensive examples and case studies
Numerical Approximation Of Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Numerical Approximation Of Partial Differential Equations written by Alfio Quarteroni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Mathematics categories.
Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).