Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm

P. A. Deift; L. C. Li

doi:10.1002/cpa.3160420704

Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm

P. A. Deift, L. C. Li

Mathematics

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

17 Scopus citations

Abstract

In [3] the authors show that the QR algorithm to compute the eigenvalues of a matrix is the integer time evaluation of a completely integrable Hamiltonian system. Here the authors show that all the associated commuting integrals generate flows that can be solved explicitly via a factorization procedure on a suitable finite, or infinite‐dimensional, Lie algebra.

Original language	English (US)
Pages (from-to)	963-991
Number of pages	29
Journal	Communications on Pure and Applied Mathematics
Volume	42
Issue number	7
DOIs	https://doi.org/10.1002/cpa.3160420704
State	Published - Oct 1989

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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title = "Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm",

abstract = "In [3] the authors show that the QR algorithm to compute the eigenvalues of a matrix is the integer time evaluation of a completely integrable Hamiltonian system. Here the authors show that all the associated commuting integrals generate flows that can be solved explicitly via a factorization procedure on a suitable finite, or infinite‐dimensional, Lie algebra.",

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AB - In [3] the authors show that the QR algorithm to compute the eigenvalues of a matrix is the integer time evaluation of a completely integrable Hamiltonian system. Here the authors show that all the associated commuting integrals generate flows that can be solved explicitly via a factorization procedure on a suitable finite, or infinite‐dimensional, Lie algebra.

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Generalized affine lie algebras and the solution of a class of flows associated with the QR eigenvalue algorithm

Abstract

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