Orthogonal polynomials, Hankel matrices, and the Lanczos algorithm

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We explore the application of the nonsymmetric Lanczos algorithm to two different problem domains, the theory of moments and orthogonal polynomials, and the factorization of Hankel matrices. The connection with a third problem domain, algorithm-based fault tolerant computing, was explored in a companion paper. We find that in the simplest case, where all leading submatrices are nonsingular, the methods reduce to classical algorithms such as the original nonsymmetric Lanczos method and the Chebyshev algorithm. We propose a back-up pivoting strategy for factorizing a Hankel matrix which avoids treating rank deficiency as a special case.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsFranklin T. Luk
PublisherPubl by Int Soc for Optical Engineering
Pages84-95
Number of pages12
ISBN (Print)0819406945
StatePublished - Dec 1 1991
EventAdvanced Signal Processing Algorithms, Architectures, and Implementations II - San Diego, CA, USA
Duration: Jul 24 1991Jul 26 1991

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume1566
ISSN (Print)0277-786X

Other

OtherAdvanced Signal Processing Algorithms, Architectures, and Implementations II
CitySan Diego, CA, USA
Period7/24/917/26/91

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