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Linear Algebra, Rational Approximation and Orthogonal Polynomials - A. Bultheel

Linear Algebra, Rational Approximation and Orthogonal Polynomials


Published: 17th November 1997
Format: PDF
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Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.

Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.

Features of this book:

? provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials

? requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.

The book will be of interest to applied mathematicians and engineers and to students and researchers.

1. Euclidean fugues -- 2. Linear algebra of Hankels -- 3. Lanczos algorithm -- 4. Orthogonal polynomials -- 5. Pade approximation -- 6. Linear systems -- 7. General rational interpolation -- 8. Wavelets.

ISBN: 9780080535524
ISBN-10: 0080535526
Format: PDF
Language: English
Published: 17th November 1997