On the Schur Decomposition of a Matrix for Parallel Computation

An algorithm to solve the eigenproblem for nonsymmetric matrices on an N × N array of mesh-connected processors, isomorphic to the architecture described by Brent and Luk for symmetric matrices, is presented. This algorithm is a generalization of the classical Jacobi method, and, as such, holds promise for parallel architectures. The rotational parameters for the nonsymmetric case are carefully analyzed; many examples of a working program, simulating the parallel architecture, are given with experimental evidence of quadratic convergence.