An acceleration method for computing the generalized eigenvalue problem on a parallel computer

AbstractWe give a cubic correction step for improving the current eigenvalue algorithms for computing the generalized Schur decomposition of a regular pencil λB−A using a Jacobi-like method. The correction method can be used to speed up the convergence at the end of the Jacobi-like process when the strictly lower triangular elements of the matrix pair (A, B) have become sufficiently small; it can be implemented in parallel on an n×n square array of mesh-connected processors in O(n) computational time. A quantitative analysis of the convergence and a comparison of the complexity of one Jacobi sweep versus one correction step are presented