Orthogonal Rational Functions

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Orthogonal Rational Functions

Author : Adhemar Bultheel
Publisher : Cambridge University Press
ISBN 13 : 0521650062
Total Pages : 423 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Orthogonal Rational Functions by : Adhemar Bultheel

Download or read book Orthogonal Rational Functions written by Adhemar Bultheel and published by Cambridge University Press. This book was released on 1999-02-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modelling and Identification with Rational Orthogonal Basis Functions

Author : Peter S.C. Heuberger
Publisher : Springer Science & Business Media
ISBN 13 : 9781852339562
Total Pages : 432 pages
Book Rating : 4.3/5 (395 download)

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Book Synopsis Modelling and Identification with Rational Orthogonal Basis Functions by : Peter S.C. Heuberger

Download or read book Modelling and Identification with Rational Orthogonal Basis Functions written by Peter S.C. Heuberger and published by Springer Science & Business Media. This book was released on 2005-06-30 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of dynamical systems are of great importance in almost all fields of science and engineering and specifically in control, signal processing and information science. A model is always only an approximation of a real phenomenon so that having an approximation theory which allows for the analysis of model quality is a substantial concern. The use of rational orthogonal basis functions to represent dynamical systems and stochastic signals can provide such a theory and underpin advanced analysis and efficient modelling. It also has the potential to extend beyond these areas to deal with many problems in circuit theory, telecommunications, systems, control theory and signal processing. Modelling and Identification with Rational Orthogonal Basis Functions affords a self-contained description of the development of the field over the last 15 years, furnishing researchers and practising engineers working with dynamical systems and stochastic processes with a standard reference work.

Orthogonal Polynomials and Special Functions

Author : Francisco Marcellàn
Publisher : Springer Science & Business Media
ISBN 13 : 3540310622
Total Pages : 432 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Francisco Marcellàn

Download or read book Orthogonal Polynomials and Special Functions written by Francisco Marcellàn and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

Orthogonal Polynomials

Author : Gabor Szeg
Publisher : American Mathematical Soc.
ISBN 13 : 0821810235
Total Pages : 448 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Orthogonal Polynomials by : Gabor Szeg

Download or read book Orthogonal Polynomials written by Gabor Szeg and published by American Mathematical Soc.. This book was released on 1939-12-31 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.

General Orthogonal Polynomials

Author : Herbert Stahl
Publisher : Cambridge University Press
ISBN 13 : 9780521415347
Total Pages : 272 pages
Book Rating : 4.4/5 (153 download)

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Book Synopsis General Orthogonal Polynomials by : Herbert Stahl

Download or read book General Orthogonal Polynomials written by Herbert Stahl and published by Cambridge University Press. This book was released on 1992-04-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.

Orthogonal Polynomials

Author : Mama Foupouagnigni
Publisher : Springer Nature
ISBN 13 : 3030367444
Total Pages : 683 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni

Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.

Orthogonal Polynomials and Special Functions

Author : Richard Askey
Publisher : SIAM
ISBN 13 : 0898710189
Total Pages : 115 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Orthogonal Polynomials and Special Functions by : Richard Askey

Download or read book Orthogonal Polynomials and Special Functions written by Richard Askey and published by SIAM. This book was released on 1975-06-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the idea that one studies orthogonal polynomials and special functions to use them to solve problems.

Orthogonal Polynomials

Author : Paul Nevai
Publisher : Springer Science & Business Media
ISBN 13 : 9400905017
Total Pages : 472 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Orthogonal Polynomials by : Paul Nevai

Download or read book Orthogonal Polynomials written by Paul Nevai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.

Orthogonal Polynomials and Painlevé Equations

Author : Walter Van Assche
Publisher : Cambridge University Press
ISBN 13 : 1108441947
Total Pages : 192 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Orthogonal Polynomials and Painlevé Equations by : Walter Van Assche

Download or read book Orthogonal Polynomials and Painlevé Equations written by Walter Van Assche and published by Cambridge University Press. This book was released on 2018 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a number of intriguing connections between Painlev equations and orthogonal polynomials, and this book is one of the first to provide an introduction to these. Researchers in integrable systems and non-linear equations will find the many explicit examples where Painlev equations appear in mathematical analysis very useful. Those interested in the asymptotic behavior of orthogonal polynomials will also find the description of Painlev transcendants and their use for local analysis near certain critical points helpful to their work. Rational solutions and special function solutions of Painlev equations are worked out in detail, with a survey of recent results and an outline of their close relationship with orthogonal polynomials. Exercises throughout the book help the reader to get to grips with the material. The author is a leading authority on orthogonal polynomials, giving this work a unique perspective on Painlev equations.

Computational Methods And Function Theory 1994 - Proceedings Of The Conference

Author : R M Ali
Publisher : World Scientific
ISBN 13 : 9814549738
Total Pages : 374 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Computational Methods And Function Theory 1994 - Proceedings Of The Conference by : R M Ali

Download or read book Computational Methods And Function Theory 1994 - Proceedings Of The Conference written by R M Ali and published by World Scientific. This book was released on 1995-10-18 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics discussed at the conference revolved around the interaction of computational methods and theoretical function theory, as well as recent advances and developments in both fields. The talks ranged from analytic function theory to approximation theory to numerical conformal mapping and other computational methods.

Operator Theory and Indefinite Inner Product Spaces

Author : Matthias Langer
Publisher : Springer Science & Business Media
ISBN 13 : 3764375167
Total Pages : 403 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Operator Theory and Indefinite Inner Product Spaces by : Matthias Langer

Download or read book Operator Theory and Indefinite Inner Product Spaces written by Matthias Langer and published by Springer Science & Business Media. This book was released on 2006-06-16 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Classical and Quantum Orthogonal Polynomials in One Variable

Author : Mourad Ismail
Publisher : Cambridge University Press
ISBN 13 : 9780521782012
Total Pages : 748 pages
Book Rating : 4.7/5 (82 download)

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Book Synopsis Classical and Quantum Orthogonal Polynomials in One Variable by : Mourad Ismail

Download or read book Classical and Quantum Orthogonal Polynomials in One Variable written by Mourad Ismail and published by Cambridge University Press. This book was released on 2005-11-21 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

Matrix Computations and Semiseparable Matrices

Author : Raf Vandebril
Publisher : JHU Press
ISBN 13 : 0801896800
Total Pages : 516 pages
Book Rating : 4.8/5 (18 download)

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Book Synopsis Matrix Computations and Semiseparable Matrices by : Raf Vandebril

Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril and published by JHU Press. This book was released on 2008-12-15 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.

Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions

Author : Tom H. Koornwinder
Publisher : Cambridge University Press
ISBN 13 : 1108916554
Total Pages : 442 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions by : Tom H. Koornwinder

Download or read book Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions written by Tom H. Koornwinder and published by Cambridge University Press. This book was released on 2020-10-15 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

An Introduction to the Approximation of Functions

Author : Theodore J. Rivlin
Publisher : Courier Corporation
ISBN 13 : 9780486640693
Total Pages : 164 pages
Book Rating : 4.6/5 (46 download)

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Book Synopsis An Introduction to the Approximation of Functions by : Theodore J. Rivlin

Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Orthogonal Functions

Author : William Jones
Publisher : CRC Press
ISBN 13 : 1000153673
Total Pages : 442 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Orthogonal Functions by : William Jones

Download or read book Orthogonal Functions written by William Jones and published by CRC Press. This book was released on 2020-12-22 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Oulines an array of recent work on the analytic theory and potential applications of continued fractions, linear functionals, orthogonal functions, moment theory, and integral transforms. Describes links between continued fractions. Pade approximation, special functions, and Gaussian quadrature."

Orthogonal Polynomials in MATLAB

Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611974305
Total Pages : 345 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Orthogonal Polynomials in MATLAB by : Walter Gautschi

Download or read book Orthogonal Polynomials in MATLAB written by Walter Gautschi and published by SIAM. This book was released on 2016-05-23 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years.?Orthogonal Polynomials in MATLAB: Exercises and Solutions?describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.?