Block-oriented J-Jacobi methods for Hermitian matrices

Two modified Jacobi methods for M-matrices

Three-Level Parallel J-Jacobi Algorithms for Hermitian Matrices

The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal load balancing between all available processors/cores is obtained. A similar blocking technique can be used to exploit local cache memory of each processor to f...

two modified jacobi methods for m-matrices

Asymptotic quadratic convergence of the serial block-Jacobi EVD algorithm for Hermitian matrices

This report is devoted to the proof of the local (asymptotic) quadratic convergence of the serial block-Jacobi EVD algorithm for Hermitian matrices with multiple eigenvalues. At each iteration step, two off-diagonal blocks with the largest Frobenius norm are annihilated which is an extension of the ‘classical’ Jacobi approach to the block case.

The Inertia of Hermitian Tridiagonal Block Matrices

Let H be a partitioned tridiagonal Hermitian matrix. We characterized the possible inertias of H by a system of linear inequalities involving the orders of the blocks, the inertia of the diagonal blocks and the ranks the lower and upper subdiagonal blocks. From the main result can be derived some propositions on inertia sets of some symmetric sign pattern matrices.