A GLOBAL CONVERGENCE PROOF FOR CYCLIC JACOBI METHODS WITH BLOCK ROTATIONS

This paper introduces a globally convergent block (column- and row-) cyclic Jacobi method for diagonalization of Hermitian matrices and for computation of the singular value decomposition of general matrices. It is shown that a block rotation (a generalization of the Jacobi 2 x 2 rotation) can be computed and implemented in a particular way to guarantee global convergence. The proof includes the convergence of the eigenspaces in the general case of multiple eigenvalues. This solves a long standing open problem of convergence of block cyclic Jacobi methods.