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The generalized Schur algorithm for the superfast solution of Toeplitz systems

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Rational Approximation and its Applications in Mathematics and Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1237))

Abstract

We review the connections between fast, O(n 2), Toeplitz solvers and the classical theory of Szegö polynomials and Schur's algorithm. We then give a concise classically motivated presentation of the superfast, O(nlog 22 n), Toeplitz solver that has recently been introduced independently by deHoog and Musicus. In particular, we describe this algorithm in terms of a generalization of Schur's classical algorithm.

Research supported in part by the National Science Foundation under grant DMS-8404980 and by the Seminar für Angewandte Mathematik of the ETH-Zürich.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, 60115, DeKalb, Illinois, U.S.A.

    Gregory S. Ammar

  2. Department of Mathematics, University of Kentucky, 40506, Lexington, Kentucky, U.S.A.

    William B. Gragg

Authors
  1. Gregory S. Ammar
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  2. William B. Gragg
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Editor information

Jacek Gilewicz Maciej Pindor Wojciech Siemaszko

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© 1987 Springer-Verlag

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Ammar, G.S., Gragg, W.B. (1987). The generalized Schur algorithm for the superfast solution of Toeplitz systems. In: Gilewicz, J., Pindor, M., Siemaszko, W. (eds) Rational Approximation and its Applications in Mathematics and Physics. Lecture Notes in Mathematics, vol 1237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072474

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  • DOI: https://doi.org/10.1007/BFb0072474

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17212-3

  • Online ISBN: 978-3-540-47412-8

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