Chebyshev type integration rules of minimum norm

Philip Rabinowitz, Nira Richter

Research output: Contribution to journalArticlepeer-review

Abstract

Equal-weight integration rules are studied in the context of certain families of Hubert spaces of analytic functions defined in a family of confocal ellipses containing the interval of integration. Rules which minimize the norm of the error functional in these spaces are shown to exist and several such rules are tabulated. Asymptotic properties of these rules are studied for ellipses shrinking to the integration interval and for ellipses expanding to cover the entire plane. In the latter case, an algebraic formulation for these asymptotic rules is given and it is shown that they agree with the classical Chebyshev integration rules whenever such rules exist.

Original languageEnglish
Pages (from-to)831-845
Number of pages15
JournalMathematics of Computation
Volume24
Issue number112
DOIs
StatePublished - Oct 1970
Externally publishedYes

Keywords

  • Analytic functions
  • Asymptotic integration rules
  • Chebyshev integration rules
  • Equal-weight integration rules
  • Hilbert space
  • Minimum norm rules
  • Norm of error functional

Fingerprint

Dive into the research topics of 'Chebyshev type integration rules of minimum norm'. Together they form a unique fingerprint.

Cite this