Bültmann & Gerriets
Orthogonal Polynomials
Computation and Approximation
von Walter Gautschi
Verlag: Hurst & Co.
Reihe: Numerical Mathematics and Scie
Gebundene Ausgabe
ISBN: 978-0-19-850672-0
Erschienen am 17.06.2004
Sprache: Englisch
Format: 232 mm [H] x 164 mm [B] x 21 mm [T]
Gewicht: 662 Gramm
Umfang: 312 Seiten

Preis: 249,50 €
keine Versandkosten (Inland)


Jetzt bestellen und voraussichtlich ab dem 21. November in der Buchhandlung abholen.

Der Versand innerhalb der Stadt erfolgt in Regel am gleichen Tag.
Der Versand nach außerhalb dauert mit Post/DHL meistens 1-2 Tage.

249,50 €
merken
klimaneutral
Der Verlag produziert nach eigener Angabe noch nicht klimaneutral bzw. kompensiert die CO2-Emissionen aus der Produktion nicht. Daher übernehmen wir diese Kompensation durch finanzielle Förderung entsprechender Projekte. Mehr Details finden Sie in unserer Klimabilanz.
Klappentext
Inhaltsverzeichnis
Biografische Anmerkung

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.



  • Basic Theory

  • 1.1: Orthogonal polynomials

  • 1.2: Properties of orthogonal polynomials

  • 1.3: Three-term recurrence relation

  • 1.4: Quadrature rules

  • 1.5: Classical orthogonal polynomials

  • 1.6: Kernal polynomials

  • 1.7: Sobolev orthogonal polynomials

  • 1.8: Orthogonal polynomials on the semicircle

  • 1.9: Notes to chapter 1

  • Computational Methods

  • 2.1: Moment-based methods

  • 2.2: Discretization methods

  • 2.3: Computing Cauchy integrals of orthogonal polynomials

  • 2.4: Modification algorithms

  • 2.5: Computing Sobolev orthogonal polynomials

  • 2.6: Notes to chapter 2

  • Applications

  • 3.1: Quadrature

  • 3.2: Least squares approximation

  • 3.3: Moment-preserving spline approximation

  • 3.4: Slowly convergent series

  • 3.5: Notes to chapter 3



Walter Gautshi is Professor Emeritus at Purdue University, USA.


weitere Titel der Reihe