Elsevier

Linear Algebra and its Applications

Volume 110, November 1988, Pages 213-242
Linear Algebra and its Applications

Self-similar flows

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Abstract

Large classes of self-similar (isospectral) flows can be viewed as continuous analogues of certain matrix eigenvalue algorithms. In particular there exist families of flows associated with the QR, LR, and Cholesky eigenvalue algorithms. This paper uses Lie theory to develop a general theory of self-similar flows which includes the QR, LR, and Cholesky flows as special cases. Also included are new families of flows associated with the SR and HR eigenvalue algorithms. The basic theory produces analogues of unshifted, single-step eigenvalue algorithms, but it is also shown how the theory can be extended to include flows which are continuous analogues of shifted and multiple-step eigenvalue algorithms.

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