Parallel Subtraction of Matrices

Characterization of parallel subtraction.

Parallel subtraction is an operation defined on pairs of positive operators. In terms of electrical networks, one may pose the following problem: Given an electrical network, represented by a specified positive operator, determine the set of positive operators which when connected in parallel with the specified operator yield another prescribed operator. The set of solutions of this electrical ...

Parallel Inversion of Polynomial Matrices

This paper presents an overview of diierent methods proposed in the last several decades for computing the inverse of a polynomial matrix, concentrating on Buss lowicz's algorithm. A detailed description of Buss lowicz's algorithm and its sequential implementation is followed by the presentation of a new parallel algorithm, based on Buss lowicz's. The distributed and shared memory versions of t...

Parallel Computation of Eigenvalues of Real Matrices

Techniques for Parallel Manipulation of Sparse Matrices

New techniques are presented forthe manipulation of sparse matrices on parallel MIMD computers. We consider the following problems: matrix addition, matrix multiplication, row and column permutation, matrix transpose, matrix vector multiplication, and Gaussian elimination.

Parallel block tridiagonalization of real symmetric matrices

Two parallel block tridiagonalization algorithms and implementations for dense real symmetric matrices are presented. Block tridiagonalization is a critical pre-processing step for the block-tridiagonal divide-and-conquer algorithm for computing eigensystems and is useful for many algorithms desiring the efficiencies of block structure in matrices. For an “effectively” sparse matrix, which freq...