Naslov
Convergence to Diagonal Form of Block Jacobi-type Methods

Autori
Hari, Vjeran

Izvornik
Numerische Mathematik (0029-599X) 129 (2015), 3; 449-481

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
eigenvalues; singular values; block Jacobi-type method; convergence

Sažetak
We provide sufficient conditions for the general sequential block Jacobi-type method to converge to the diagonal form for cyclic pivot strategies which are weakly equivalent to the column-cyclic strategy. Given a block-matrix partition $(A_{; ; ; ; ; ; ; ij}; ; ; ; ; ; ; )$ of a square matrix $\bA$, the paper analyzes the iterative process of the form $\bA^{; ; ; ; ; ; ; (k+1)}; ; ; ; ; ; ; = [\bP^{; ; ; ; ; ; ; (k)}; ; ; ; ; ; ; ]^*\, \bA^{; ; ; ; ; ; ; (k)}; ; ; ; ; ; ; \, \bQ^{; ; ; ; ; ; ; (k)}; ; ; ; ; ; ; $, $k\geq 0$, $\bA^{; ; ; ; ; ; ; (0)}; ; ; ; ; ; ; =\bA$, where $\bP^{; ; ; ; ; ; ; (k)}; ; ; ; ; ; ; $ and $\bQ^{; ; ; ; ; ; ; (k)}; ; ; ; ; ; ; $ are elementary block matrices which differ from the identity matrix in four blocks, two diagonal and the two corresponding off-diagonal blocks. In our analysis of convergence a promising new tool is used, namely, the theory of block Jacobi operators. Typical applications lie in proving the global convergence of block Jacobi-type methods for solving standard and generalized eigenvalue and singular value problems.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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