Self-equivalent flows associated with the generalized eigenvalue problem

We present a family of flows which includes continuous analogues of the unshifted and shifted LZ and QZ algorithms for the generalized eigenvalue problem. In order to do this we use elementary Lie theory to create a general family of algorithms, of which the LZ and QZ algorithms are special cases. F...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 118; pp. 107 - 127
Main Authors Watkins, D.S., Elsner, L.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.1989
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Summary:We present a family of flows which includes continuous analogues of the unshifted and shifted LZ and QZ algorithms for the generalized eigenvalue problem. In order to do this we use elementary Lie theory to create a general family of algorithms, of which the LZ and QZ algorithms are special cases. For each such algorithm we construct a family of associated flows, some of which are interpolants of the algorithm. We do not restrict our attention to Hessenberg-triangular forms; we consider arbitrary pairs of nonsingular matrices.
ISSN:0024-3795
1873-1856
DOI:10.1016/0024-3795(89)90576-4