Linear algebra, rational approximation, and orthogonal polynomials [EBook] / Adhemar Bultheel, Marc van Barel.
Linear algebra, rational approximation, and orthogonal polynomials [EBook] / Adhemar Bultheel, Marc van Barel.
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, nonnormal Pade tables, lookahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algor...
Personal Name(s):  Bultheel, Adhemar. 

Barel, Marc van,  
Imprint: 
Amsterdam ; New York :
Elsevier,
1997

Physical Description: 
1 online resource (xvii, 446 p.) : ill. 
Note: 
englisch 
ISBN: 
0444828729 0080535526 9780444828729 9780080535524 
Series Title: 
Studies in computational mathematics ;
6 
Subject (LOC):  
Full Text 
Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, nonnormal Pade tables, lookahead 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 biorthogonal polynomials, minimal Pade 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: & bull; provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials & bull; 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. 