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Rational approximants associated with measures supported on the unit circle and the real line

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
236
Issue
1
Identifiers
DOI: 10.1016/j.cam.2011.05.042
Keywords
  • Markov Function
  • Orthogonal Polynomials
  • Quadrature Formulas
  • Padé Approximants
  • Error Estimates
  • Convergence

Abstract

Abstract As a continuation of the well known connection between the theory of orthogonal polynomials on the unit circle and the interval [ − 1 , 1 ] , in this paper properties concerning error and convergence of certain rational approximants associated with the measures d μ ( t ) and d σ ( θ ) = | d μ ( cos θ ) | supported on [ − 1 , 1 ] and the unit circle respectively are deduced. Numerical illustrations are also given.

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