Self-equivalent flows associated with the generalized eigenvalue problem
The authors use elementary Lie theory to develop a family of algorithms for solving the generalized eigenvalue problem \(Ax=\lambda Bx\) for arbitrary pairs of nonsingular matrices. The family (referred as FGZ algorithms) includes the well known LZ algorithm of \textit{L. Kaufman} [SIAM J. Numer. Anal. 11, 997-1024 (1974; Zbl 0294.65025)] and the QZ algorithm of \textit{C. B. Moler} and \textit{G. W. Stewart} [SIAM J. Numer. Anal. 10, 241-256 (1973; Zbl 0225.65046)], as well as new algorithms called SZ and HZ. The continuous analogues of the unshifted and shifted LZ and QZ algorithms are presented. For each considered algorithm a family of associated flows is constructed.
scientific article; zbMATH DE number 4121302
scientific article