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Iterated solutions of linear operator equations with the Tau method


Authors: M. K. El-Daou and H. G. Khajah
Journal: Math. Comp. 66 (1997), 207-213
MSC (1991): Primary 41A10, 41A65; Secondary 45B05, 47A50
MathSciNet review: 1377662
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.


References [Enhancements On Off] (What's this?)

  • 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. MR 0405049
  • 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. MR 664597
  • 3. Eduardo L. Ortiz, The tau method, SIAM J. Numer. Anal. 6 (1969), 480–492. MR 0258287
  • 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. MR 0474847

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Additional Information

M. K. El-Daou
Affiliation: Applied Sciences Department, College of Technical Studies, Paaet, P. O. Box 42325, Shuwaikh 70654, Kuwait

H. G. Khajah
Affiliation: Applied Sciences Department, College of Technical Studies, Paaet, P. O. Box 42325, Shuwaikh 70654, Kuwait
Email: hkhajah@kuc01.kuniv.edu.kw

DOI: http://dx.doi.org/10.1090/S0025-5718-97-00803-X
Keywords: Tau Method, polynomial approximation, linear operator equations
Received by editor(s): July 27, 1995
Article copyright: © Copyright 1997 American Mathematical Society