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Iterated solutions of linear operator equations with the Tau method. (English) Zbl 0855.47006
Summary: The Tau method produces polynomial approximations of solutions of differential equations. The purpose of this paper is
(i) to extend the recursive formulation of this method to general linear operator equations defined in a separable Hilbert space, and
(ii) to develop an iterative refinement procedure which improves on the accuracy of Tau approximations.
Applications to Fredholm integral equations demonstrate the effectiveness of this technique.

MSC:
47A50 Equations and inequalities involving linear operators, with vector unknowns
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A10 Approximation by polynomials
45B05 Fredholm integral equations
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[1] Mischa Cotlar and Roberto Cignoli, An introduction to functional analysis, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1974. Translated from the Spanish by A. Torchinsky and A. González Villalobos; North-Holland Texts in Advanced Mathematics. · Zbl 0277.46001
[2] L. V. Kantorovich and G. P. Akilov, Functional analysis, 2nd ed., Pergamon Press, Oxford-Elmsford, N.Y., 1982. Translated from the Russian by Howard L. Silcock. · Zbl 0484.46003
[3] Eduardo L. Ortiz, The tau method, SIAM J. Numer. Anal. 6 (1969), 480 – 492. · Zbl 0195.45701 · doi:10.1137/0706044 · doi.org
[4] Eduardo L. Ortiz, Canonical polynomials in the Lanczos tau method, Studies in numerical analysis (papers in honour of Cornelius Lanczos on the occasion of his 80th birthday), Academic Press, London, 1974, pp. 73 – 93. · Zbl 0325.41004
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