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.
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© 1988 D. Reidel Publishing Company
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Jones, W.B. (1988). Schur’s Algorithm Extended and Schur Continued Fractions. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation. Mathematics and Its Applications, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2901-2_17
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DOI: https://doi.org/10.1007/978-94-009-2901-2_17
Publisher Name: Springer, Dordrecht
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