Applications And Computation Of Orthogonal Polynomials
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Applications And Computation Of Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-01
Applications And Computation Of Orthogonal Polynomials written by Walter Gautschi 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 1999-07-01 with Mathematics categories.
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.
Applications And Computation Of Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Applications And Computation Of Orthogonal Polynomials written by Walter Gautschi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The workshop on Applications and Computation of Orthogonal Polynomials took place March 22-28, 1998 at the Oberwolfach Mathematical Research Institute. It was the first workshop on this topic ever held at Oberwolfach. There were 46 participants from 13 countries, more than half coming from Germany and the United States, and a substantial number from Italy. A total of 23 plenary lectures were presented and 4 short informal talks. Open problems were discussed during an evening session. This volume contains refereed versions of 18 papers presented at, or submitted to, the conference. The theory of orthogonal polynomials, as a branch of classical analysis, is well established. But orthogonal polynomials play also an important role in many areas of scientific computing, such as least squares fitting, numerical integration, and solving linear algebraic systems. Though the basic tenets have their roots in 19th century mathematics, the use of modern computers has required the development and study of new algorithms that are accurate and robust. The computational methods and applications represented in this volume, of necessity, are incomplete, yet sufficiently varied to convey an impression of current activities in this area.
An Introduction To Orthogonal Polynomials
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Author : Theodore S Chihara
language : en
Publisher: Courier Corporation
Release Date : 2011-02-17
An Introduction To Orthogonal Polynomials written by Theodore S Chihara and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-17 with Mathematics categories.
"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--
Orthogonal Polynomials
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Author : Walter Gautschi
language : en
Publisher: Oxford University Press on Demand
Release Date : 2004
Orthogonal Polynomials written by Walter Gautschi and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative to a positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods and discretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapter deals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appended to each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.
Classical And Quantum Orthogonal Polynomials In One Variable
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Author : Mourad Ismail
language : en
Publisher: Cambridge University Press
Release Date : 2005-11-21
Classical And Quantum Orthogonal Polynomials In One Variable written by Mourad Ismail 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 2005-11-21 with Mathematics categories.
The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.
Orthogonal Polynomials And Special Functions
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Author : Francisco Marcellàn
language : en
Publisher: Springer
Release Date : 2006-10-18
Orthogonal Polynomials And Special Functions written by Francisco Marcellàn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-18 with Mathematics categories.
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? The present set of lecture notes contains seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions.
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.
Orthogonal Polynomials Of Several Variables
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Author : Charles F. Dunkl
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-21
Orthogonal Polynomials Of Several Variables written by Charles F. Dunkl 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 2014-08-21 with Mathematics categories.
Updated throughout, this revised edition contains 25% new material covering progress made in the field over the past decade.
Topics In Polynomials Of One And Several Variables And Their Applications
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Author : Themistocles M. Rassias
language : en
Publisher: World Scientific
Release Date : 1993
Topics In Polynomials Of One And Several Variables And Their Applications written by Themistocles M. Rassias and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
Acta Numerica 1996 Volume 5
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 1996-07-25
Acta Numerica 1996 Volume 5 written by Arieh Iserles 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 1996-07-25 with Mathematics categories.
Acta Numerica is an annual volume presenting survey papers in numerical analysis. Each year the editorial board selects significant topics and invites papers from authors who have made notable contributions to the development of that topic. The articles are intended to summarize the field at a level accessible to graduate students and researchers. Acta Numerica has proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of the subject and follow developments, but also as an advanced teaching aid at colleges and universities. Articles in previous volumes have been expanded into both monographs and textbooks, and many of the original articles themselves have been used as the prime resource for graduate courses.