On One-Sided Jacobi Methods for Parallel Computation

Abstract

Convergence proofs are given for one-sided Jacobi/Hestenes methods for the singular value problem. The limiting form of the matrix iterates for the Hestenes method with optimization when the original matrix is normal is derived; this limiting matrix is block diagonal, where the blocks are multiples of unitary matrices. A variation in the algorithm to guarantee convergence to a diagonal matrix for the symmetric eigenvalue problem is shown. Implementation techniques for parallel computation, in particular, on the hypercube are indicated.