Orthogonal Series And Approximation Of Functions
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Orthogonal Series And Approximation Of Functions
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Author : Sergej Michajlovic Nikol'skij
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-15
Orthogonal Series And Approximation Of Functions written by Sergej Michajlovic Nikol'skij and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-15 with Mathematics categories.
Orthogonal Functions In Systems And Control
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Author : Kanti Bhushan Datta
language : en
Publisher: World Scientific
Release Date : 1995
Orthogonal Functions In Systems And Control written by Kanti Bhushan Datta and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book provides a systematic and unified approach to the analysis, identification and optimal control of continuous-time dynamical systems via orthogonal polynomials such as Legendre, Laguerre, Hermite, Tchebycheff, Jacobi, Gegenbauer, and via orthogonal functions such as sine-cosine, block-pulse, and Walsh. This is the first book devoted to the application of orthogonal polynomials in systems and control, establishing the superiority of orthogonal polynomials to other orthogonal functions.
Orthogonal Rational Functions
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Author : Adhemar Bultheel
language : en
Publisher: Cambridge University Press
Release Date : 1999-02-13
Orthogonal Rational Functions written by Adhemar Bultheel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-13 with Mathematics categories.
This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.
An Introduction To The Approximation Of Functions
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Author : Theodore J. Rivlin
language : en
Publisher: Courier Corporation
Release Date : 1981-01-01
An Introduction To The Approximation Of Functions written by Theodore J. Rivlin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Numerical Methods Iii Approximation Of Functions
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Author : Boris Obsieger
language : en
Publisher: university-books.eu
Release Date : 2013-10-25
Numerical Methods Iii Approximation Of Functions written by Boris Obsieger and has been published by university-books.eu this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-25 with Mathematics categories.
The book is written primarily for the students on technical universities, but also as a useful handbook for engineers and PhD students. It introduces reader into various types of approximations of functions, which are defined either explicitly or by their values in the distinct set of points, as well as into economisation of existing approximation formulas. Why the approximation of functions is so important? Simply because various functions cannot be calculated without approximation. Approximation formulas for some of these functions (such as trigonometric functions and logarithms) are already implemented in the calculators and standard computer libraries, providing the precision to all bits of memory in which a value is stored. So high precision is not usually required in the engineering practice, and use more numerical operations that is really necessary. Economised approximation formulas can provide required precision with less numerical operation, and can made numerical algorithms faster, especially when such formulas are used in nested loops. The other important use of approximation is in calculating functions that are defined by values in the chosen set of points, such as in solving integral equations (usually obtained from differential equations). The book is divided into five chapters. In the first chapter are briefly explained basic principles of approximations, i.e. approximations near the chosen point (by Maclaurin, Taylor or Padé expansion), principles of approximations with orthogonal series and principles of least squares approximations. In the second chapter, various types of least squares polynomial approximations, particularly those by using orthogonal polynomials such as Legendre, Jacobi, Laguerre, Hermite, Zernike and Gram polynomials are explained. Third chapter explains approximations with Fourier series, which are the base for developing approximations with Chebyshev polynomials (fourth chapter). Uniform approximation and further usage of Chebyshev polynomials in the almost uniform approximation, as well as in economisation of existing approximation formulas, are described in fifth chapter. Practical applications of described approximation procedures are supported by 35 algorithms and 40 examples. Besides its practical usage, the given text with 36 figures and 11 tables, partially in colour, represents a valuable background for understanding, developing and applying various numerical methods, such as interpolation, numerical integration and solving partial differential equations, which are topics in the further volumes of the series Numerical Methods.
Mathematical Analysis
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Author : L. A. Lyusternik
language : en
Publisher: Elsevier
Release Date : 2014-07-15
Mathematical Analysis written by L. A. Lyusternik and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Mathematics categories.
Mathematical Analysis: Functions, Limits, Series, Continued Fractions provides an introduction to the differential and integral calculus. This book presents the general problems of the theory of continuous functions of one and several variables, as well as the theory of limiting values for sequences of numbers and vectors. Organized into six chapters, this book begins with an overview of real numbers, the arithmetic linear continuum, limiting values, and functions of one variable. This text then presents the theory of series and practical methods of summation. Other chapters consider the theory of numerical series and series of functions and other analogous processes, particularly infinite continued fractions. This book discusses as well the general problems of the reduction of functions to orthogonal series. The final chapter deals with constants and the most important systems of numbers, including Bernoulli and Euler numbers. This book is a valuable resource for mathematicians, engineers, and research workers.
Methods Of Approximation Theory
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Author : Alexander I. Stepanets
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Methods Of Approximation Theory written by Alexander I. Stepanets and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
No detailed description available for "Methods of Approximation Theory".
Convergence Problems Of Orthogonal Series
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Author : G. Alexits
language : en
Publisher: Elsevier
Release Date : 2014-07-23
Convergence Problems Of Orthogonal Series written by G. Alexits and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Mathematics categories.
Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.
Interpolation And Approximation
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Author : Philip J. Davis
language : en
Publisher: Courier Corporation
Release Date : 1975-01-01
Interpolation And Approximation written by Philip J. Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-01-01 with Mathematics categories.
Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
The Volterra Series And Its Application
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Author : Mark Dunn
language : en
Publisher: Lulu.com
Release Date : 2015-04-10
The Volterra Series And Its Application written by Mark Dunn and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-10 with Technology & Engineering categories.
Modeling of weakly nonlinear systems by means of Volterra series analysis is presented. Necessary conditions for representing nonlinearities by a Volterra series are developed analytically as well as heuristically. A two-condition convergence criterion for Volterra series and a method for determining Volterra transfer functions are established. For systems with multiple nodes, an extension of Volterra series analysis; method of nonlinear currents is developed and applied to a MESFET amplifier. Finally, methods of quantifying nonlinear behavior are discussed.