Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal PadAc 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 PadAc 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: ac provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials ac 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.One can derive from these results for real polynomials also results for complex polynomials, or get information about the location of the zeros with respect to a half plane or a circle. See for example . We shall not elaborate this here, but anbsp;...
|Title||:||Linear Algebra, Rational Approximation and Orthogonal Polynomials|
|Author||:||A. Bultheel, M. Van Barel|
|Publisher||:||Elsevier - 1997-11-17|