A Global Convergence Proof for Cyclic Jacobi Methods with Block Rotations

Authors:
Zlatko Drmač
Affiliations:
drmac@math.hr
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2009

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Abstract

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 $2\times2$ 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.