A KQZ algorithm for solving linear-response eigenvalue equations

Ulrike Flaschka*, Wen-Wei Lin, Jy Liang Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We develop a new algorithm, KQZ, for solving the generalized eigenvalue problem Mx=λLx which comes from the linear-response (LR) eigenvalue equation. In contrast to the QZ algorithm, our algorithm preserves the block structure of the pencil M-λL during the computations and only uses K-orthogonal transformations. We accelerate the convergence by using a quadruple implicit-shift technique based on the implicit KQ theorem. The KQZ algorithm saves about half the computational cost and storage of the QZ algorithm.

Original languageEnglish
Pages (from-to)93-123
Number of pages31
JournalLinear Algebra and Its Applications
Issue numberC
StatePublished - 1 Mar 1992

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