Extremal Polynomials with Application to Richardson Iteration for Indefinite Linear Systems.

Abstract

The application of Richardson iteration to a symmetric, but indefinite linear system requires certain parameters which can be determined from the zeros in the error of a certain best polynomial approximant on some set S known to contain the spectrum of the coefficient matrix. It is pointed out that this error can also be obtained as a multiple of the extremal polynomial for the linear functional p at p(0), and this leads to an efficient Remes type algorithm for its determination. A program incorporating this algorithm for the case that S consists of two intervals bracketing zero is also given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1980
Accession Number
ADA093568

Entities

People

  • Carl R. de Boor
  • John R. Rice

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Chebyshev Approximations
  • Chebyshev Polynomials
  • Coefficients
  • Computations
  • Construction
  • Convergence
  • Differential Equations
  • Equations
  • Linear Systems
  • Mathematics
  • Partial Differential Equations
  • Polynomials
  • Sequences
  • Simultaneous Equations
  • Slope
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra