A quadratically convergent parallel Jacobi process for diagonally dominant matrices with distinct eigenvalues

摘要

This paper discusses a generalization for non-Hermitian matrices of the Jacobi eigenvalue process (1846). In each step 12n pairs of nondiagonal elements are annihilated in an almost diagonal matrix with distinct eigenvalues. We prove that the recursively constructed sequence of matrices converges to a diagonal matrix. As in the classical Jacobi method the convergence is quadratic and the process is adapted to parallel implementation on an array processor or a hypercube.