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 (generalization of the Jacobi’s 2× 2 rotation) must be computed and implemented in a particular way to guarantee global convergence. This solves a long standing open problem of convergence of block cyclic Jacobi methods. The proof includes the convergence of the eigenspaces in the general case of multiple eigenvalues.