Orthogonal polynomials, Hankel matrices, and the Lanczos algorithm

Daniel L. Boley

doi:10.1117/12.49814

1 December 1991 Orthogonal polynomials, Hankel matrices, and the Lanczos algorithm

Daniel L. Boley

Proceedings Volume 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II; (1991) https://doi.org/10.1117/12.49814
Event: San Diego, '91, 1991, San Diego, CA, United States

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.

Citation Download Citation

Daniel L. Boley "Orthogonal polynomials, Hankel matrices, and the Lanczos algorithm", Proc. SPIE 1566, Advanced Signal Processing Algorithms, Architectures, and Implementations II, (1 December 1991); https://doi.org/10.1117/12.49814

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