engleski

On Block Jacobi Annihilators

The paper reveals the structure of the block Jacobi annihilator associated with one step of the general block Jacobi-type process of the form $\bA^{; ; ; ; (k+1)}; ; ; ; = [\bP^{; ; ; ; (k)}; ; ; ; ]^*\, \bA^{; ; ; ; (k)}; ; ; ; \, \bQ^{; ; ; ; (k)}; ; ; ; $, $k\geq 0$. Here $\bP^{; ; ; ; (k)}; ; ; ; $ and $\bQ^{; ; ; ; (k)}; ; ; ; $ are nonsingular elementary block-matrices which differ from the identity in four blocks: two diagonal and the two corresponding off-diagonal blocks. In the case of unitary $\bP^{; ; ; ; (k)}; ; ; ; $ and $\bQ^{; ; ; ; (k)}; ; ; ; $, the block Jacobi annihilator is up to a permutational similarity a direct sum of an identity matrix, of a zero matrix and of a unitary matrix. The block Jacobi annihilators are building blocks of the block Jacobi operators, which are used in proving the global convergence of block Jacobi-type processes.

eigenvalues ; singular value ; block Jacobi-type method ; global convergence

nije evidentirano