A fast method to diagonalize a Hankel matrix

Daniel L. Boley; Franklin T. Luk; David Vandevoorde

doi:10.1016/S0024-3795(98)10101-5

A fast method to diagonalize a Hankel matrix

Daniel L. Boley, Franklin T. Luk, David Vandevoorde

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We consider a Vandermonde factorization of a Hankel matrix, and propose a new approach to compute the full decomposition in O(n²) operations. The method is based on the use of a variant of the Lanczos method to compute a tridiagonal matrix whose eigenvalues are the modes generating the entries in the Hankel matrix. By adapting existing methods to solve for these eigenvalues and then for the coefficients, one arrives at a method to compute the entire decomposition in O(n²) operations. The method is illustrated with a simple numerical example.

Original language	English (US)
Pages (from-to)	41-52
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	284
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(98)10101-5
State	Published - Nov 15 1998

Bibliographical note

Funding Information:
author. E-mail: [email protected]. was partially supported by NSF Grants CCR-9405380 and CCR-9628786.

Keywords

Hankel matrix
Lanczos algorithm
Prony's method
Vandermonde decomposition

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10.1016/S0024-3795(98)10101-5

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title = "A fast method to diagonalize a Hankel matrix",

abstract = "We consider a Vandermonde factorization of a Hankel matrix, and propose a new approach to compute the full decomposition in O(n2) operations. The method is based on the use of a variant of the Lanczos method to compute a tridiagonal matrix whose eigenvalues are the modes generating the entries in the Hankel matrix. By adapting existing methods to solve for these eigenvalues and then for the coefficients, one arrives at a method to compute the entire decomposition in O(n2) operations. The method is illustrated with a simple numerical example.",

keywords = "Hankel matrix, Lanczos algorithm, Prony's method, Vandermonde decomposition",

author = "Boley, {Daniel L.} and Luk, {Franklin T.} and David Vandevoorde",

note = "Funding Information: author. E-mail: [email protected]. was partially supported by NSF Grants CCR-9405380 and CCR-9628786.",

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T1 - A fast method to diagonalize a Hankel matrix

AU - Boley, Daniel L.

AU - Luk, Franklin T.

AU - Vandevoorde, David

N1 - Funding Information: author. E-mail: [email protected]. was partially supported by NSF Grants CCR-9405380 and CCR-9628786.

PY - 1998/11/15

Y1 - 1998/11/15

N2 - We consider a Vandermonde factorization of a Hankel matrix, and propose a new approach to compute the full decomposition in O(n2) operations. The method is based on the use of a variant of the Lanczos method to compute a tridiagonal matrix whose eigenvalues are the modes generating the entries in the Hankel matrix. By adapting existing methods to solve for these eigenvalues and then for the coefficients, one arrives at a method to compute the entire decomposition in O(n2) operations. The method is illustrated with a simple numerical example.

AB - We consider a Vandermonde factorization of a Hankel matrix, and propose a new approach to compute the full decomposition in O(n2) operations. The method is based on the use of a variant of the Lanczos method to compute a tridiagonal matrix whose eigenvalues are the modes generating the entries in the Hankel matrix. By adapting existing methods to solve for these eigenvalues and then for the coefficients, one arrives at a method to compute the entire decomposition in O(n2) operations. The method is illustrated with a simple numerical example.

KW - Hankel matrix

KW - Lanczos algorithm

KW - Prony's method

KW - Vandermonde decomposition

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DO - 10.1016/S0024-3795(98)10101-5

M3 - Article

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VL - 284

SP - 41

EP - 52

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

A fast method to diagonalize a Hankel matrix

Abstract

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