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Multivariate Polynomial Approximation

  • Manfred Reimer

Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 144)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Manfred Reimer
      Pages 3-18
    3. Manfred Reimer
      Pages 19-38
  3. Approximation Means

    1. Front Matter
      Pages 39-39
    2. Manfred Reimer
      Pages 41-66
    3. Manfred Reimer
      Pages 67-108
  4. Multivariate Approximation

    1. Front Matter
      Pages 109-109
    2. Manfred Reimer
      Pages 111-178
    3. Manfred Reimer
      Pages 179-262
    4. Manfred Reimer
      Pages 263-282
  5. Applications

    1. Front Matter
      Pages 283-283
    2. Manfred Reimer
      Pages 285-303
  6. Back Matter
    Pages 305-358

About this book

Introduction

Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

Keywords

Tomography approximation theory integral transform interpolation numerical analysis

Authors and affiliations

  • Manfred Reimer
    • 1
  1. 1.Fachbereich MathematikUniversität DortmundDortmundGermany

Bibliographic information

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