Linear Algebra, Rational Approximation and Orthogonal PolynomialsBy
- A. Bultheel
- M. Van Barel, Katholieke Universiteit Leuven, Heverlee, Belgium
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.
Studies in Computational Mathematics
Published: November 1997
...This book will be a major reference book for people working in these areas and also mark a starting point for future research.
V. Mehrmann, Newsletter on Computational Applied Mathematics, Vol.16, No.1, March 1999
...An important addition to the literature...I recommend it to anyone who is interested not only in approximation theory but in tts applications in engineering and computer science.
Journal of Approximation Theory, 1999
- Preface. Table of contents. List of symbols. 1. Euclidean fugues. 2. Linear algebra of Hankels. 3. Lanczos algorithm. 4. Orthogonal polynomials. 5. Padé approximation. 6. Linear systems. 7. General rational interpolation. 8. Wavelets. Bibliography. List of algorithms. Index.