MTU Cork Library Catalogue

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An introduction to the approximation of functions / Theodore J. Rivlin.

By: Rivlin, Theodore J, 1926-2006.
Material type: materialTypeLabelBookPublisher: New York : London : Dover ; Constable, 1981, c1969Description: viii, 150 p. : il.l ; 21 cm. + pbk.ISBN: 0486640698.Subject(s): Functions, Continuous | Approximation theoryDDC classification: 515.7
Contents:
Introduction -- Uniform approximation -- Least-squares approximation -- Least-first-power approximation -- Polynomial and spline interpolation -- Approximation and interpolation by rational functions.

Enhanced descriptions from Syndetics:

This graduate-level text offers a concise but wide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particular emphasis on approximation by polynomials and not only discusses the theoretical underpinnings of many common algorithms but also demonstrates their practical applications. 1969 edition.

Bibliography: (pages 143-147) and index.

Introduction -- Uniform approximation -- Least-squares approximation -- Least-first-power approximation -- Polynomial and spline interpolation -- Approximation and interpolation by rational functions.

Table of contents provided by Syndetics

  • Introduction (p. 1)
  • General Existence and Uniqueness of Approximations
  • Exercises (p. 8)
  • Chapter 1 Uniform Approximation (p. 11)
  • 1.1 Uniform Approximation by Polynomials (p. 11)
  • 1.1.1 The Weierstrass Theorem and Bernstein Polynomial Approximation (p. 11)
  • 1.1.2 Jackson's Theorems (p. 17)
  • 1.2 Characterization of Best Approximations (p. 24)
  • 1.3 Approximation on a Finite Set of Points (p. 33)
  • 1.4 Computational Methods (p. 40)
  • 1.4.1 The Exchange Method (p. 40)
  • 1.4.2 Linear Programming (p. 42)
  • Exercises (p. 43)
  • Chapter 2 Least-Squares Approximation (p. 48)
  • 2.1 Approximation on an Interval (p. 48)
  • 2.2 The Jacobi Polynomials (p. 52)
  • 2.3 Approximation on a Finite Set of Points (p. 55)
  • 2.4 Effectiveness as a Uniform Approximation (p. 57)
  • Exercises (p. 61)
  • Chapter 3 Least-First-Power Approximation (p. 66)
  • 3.1 Approximation on an Interval (p. 66)
  • 3.2 Approximation on a Finite Set of Points (p. 73)
  • 3.3 Some Computational Aspects (p. 78)
  • Exercises (p. 83)
  • Chapter 4 Polynomial and Spline Interpolation (p. 87)
  • 4.1 General Results (p. 87)
  • 4.2 The Size of the Lebesgue Constants (p. 90)
  • 4.3 Interpolating Polynomials as Least-Squares and Least-First-Power Approximations (p. 101)
  • 4.4 Interpolation and Approximation by Splines (p. 104)
  • 4.4.1 Spline Interpolation (p. 104)
  • 4.4.2 Some Extremal Properties of Splines (p. 108)
  • 4.4.3 Uniform Approximation by Splines (p. 110)
  • 4.4.4 Least-Squares Approximation by Splines (p. 113)
  • Exercises (p. 114)
  • Chapter 5 Approximation and Interpolation by Rational Functions (p. 120)
  • 5.1 Existence, Characterization, and Uniqueness (p. 120)
  • 5.2 Degree of Approximation (p. 128)
  • 5.3 Finite Point Sets (p. 130)
  • 5.4 Rational Interpolation (p. 132)
  • 5.5 Computing a Best Approximation (p. 135)
  • Exercises (p. 138)
  • Bibliography (p. 143)
  • Index (p. 149)

Author notes provided by Syndetics

Theodore J. Rivlin was a Research Staff Member in the Department of Mathematical Sciences at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York.

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