A global convergence proof of cyclic Jacobi methods with block rotations LAPACK Working Note 196
Zlatko Drmač · 2007
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.