Schur’s Algorithm Extended and Schur Continued Fractions

  • William B. Jones
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 43)

Abstract

A generalization of Schur’s algorithm is given which provides rational interpolants at a sequence of (not necessarily distinct) points in the complex plane. The algorithm can easily be extended to functions of several variables. It is also shown that Schur continued fractions with γ0 ≠ 0 are equivalent to Perron-Carathéodory (PC-) fractions. This connection is used to obtain new formulas for the Schur parameters γn and a new characterization of positive Schur continued fractions. Continued fraction methods are used to prove convergence and obtain truncation error bounds for Schur approximants.

Keywords

Continue Fraction Digital Filter Algorithm Extend Determinant Formula Rational Interpolants 
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Copyright information

© D. Reidel Publishing Company 1988

Authors and Affiliations

  • William B. Jones
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

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