Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem
Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem
A generic $GZ$ algorithm for the generalized eigenvalue problem $Ax = \lambda Bx$ is presented. This is actually a large class of algorithms that includes multiple-step $QZ$ and $LZ$ algorithms, as well as $QZ$-$LZ$ hybrids, as special cases. First the convergence properties of the $GZ$ algorithm are discussed, then a …