The Lanczos algorithm and Hankel matrix factorization

Daniel L. Boley; Tong J. Lee; Franklin T. Luk

doi:10.1016/0024-3795(92)90022-3

The Lanczos algorithm and Hankel matrix factorization

Daniel L. Boley, Tong J. Lee, Franklin T. Luk

Computer Science and Engineering

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Abstract

We explore the connections between the Lanczos algorithm for matrix tridiagonalization and two fast algorithms for Hankel matrix factorization. We show how the asymmetric Lanczos process is related to the Berlekamp-Massey algorithm, and how the symmetrized Lanczos process is related to the Phillips algorithm. We also discuss conditions under which the analysis of Phillips applies.

Original language	English (US)
Pages (from-to)	109-133
Number of pages	25
Journal	Linear Algebra and Its Applications
Volume	172
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(92)90022-3
State	Published - Jul 15 1992

Bibliographical note

Funding Information:
The authors acknowledget heir researchs ponsors:D . L. Boley was supported in part by the rattan ScienceF ~ndat~~ under grant CCR”8813~93 and by the Minnesota SupercomputerIn stitute, T. J. Lee by an Intel Foundation Cradu-ate Fellowship, and F. T. Luk by the Army Research Office under contract D~L~3-90-~~10~, The aut~rs a&o thank Adam B~an~~yka nd Douglas Sweetj ii valuable discussions.

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title = "The Lanczos algorithm and Hankel matrix factorization",

abstract = "We explore the connections between the Lanczos algorithm for matrix tridiagonalization and two fast algorithms for Hankel matrix factorization. We show how the asymmetric Lanczos process is related to the Berlekamp-Massey algorithm, and how the symmetrized Lanczos process is related to the Phillips algorithm. We also discuss conditions under which the analysis of Phillips applies.",

author = "Boley, {Daniel L.} and Lee, {Tong J.} and Luk, {Franklin T.}",

note = "Funding Information: The authors acknowledget heir researchs ponsors:D . L. Boley was supported in part by the rattan ScienceF ~ndat~~ under grant CCR”8813~93 and by the Minnesota SupercomputerIn stitute, T. J. Lee by an Intel Foundation Cradu-ate Fellowship, and F. T. Luk by the Army Research Office under contract D~L~3-90-~~10~, The aut~rs a&o thank Adam B~an~~yka nd Douglas Sweetj ii valuable discussions.",

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AU - Boley, Daniel L.

AU - Lee, Tong J.

AU - Luk, Franklin T.

N1 - Funding Information: The authors acknowledget heir researchs ponsors:D . L. Boley was supported in part by the rattan ScienceF ~ndat~~ under grant CCR”8813~93 and by the Minnesota SupercomputerIn stitute, T. J. Lee by an Intel Foundation Cradu-ate Fellowship, and F. T. Luk by the Army Research Office under contract D~L~3-90-~~10~, The aut~rs a&o thank Adam B~an~~yka nd Douglas Sweetj ii valuable discussions.

PY - 1992/7/15

Y1 - 1992/7/15

N2 - We explore the connections between the Lanczos algorithm for matrix tridiagonalization and two fast algorithms for Hankel matrix factorization. We show how the asymmetric Lanczos process is related to the Berlekamp-Massey algorithm, and how the symmetrized Lanczos process is related to the Phillips algorithm. We also discuss conditions under which the analysis of Phillips applies.

AB - We explore the connections between the Lanczos algorithm for matrix tridiagonalization and two fast algorithms for Hankel matrix factorization. We show how the asymmetric Lanczos process is related to the Berlekamp-Massey algorithm, and how the symmetrized Lanczos process is related to the Phillips algorithm. We also discuss conditions under which the analysis of Phillips applies.

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JO - Linear Algebra and Its Applications

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The Lanczos algorithm and Hankel matrix factorization

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