engleski

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 $2\times 2$ 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.

eigenvalues; convergence; Jacobi method

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