Stabilized bordered block diagonal forms for parallel sparse solvers

Authors:
Iain S. Duff;Jennifer A. Scott
Affiliations:
Computational Science and Engineering Department, Atlas Centre, Rutherford Appleton Laboratory, Oxon, UK;Computational Science and Engineering Department, Atlas Centre, Rutherford Appleton Laboratory, Oxon, UK
Venue:
Parallel Computing
Year:
2005

Citing 6
Cited 0

Partitioning mathematical programs for parallel solution

Mathematical Programming: Series A and B
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices

SIAM Journal on Matrix Analysis and Applications
On Algorithms for Obtaining a Maximum Transversal

ACM Transactions on Mathematical Software (TOMS)
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]

ACM Transactions on Mathematical Software (TOMS)
A parallel direct solver for large sparse highly unsymmetric linear systems

ACM Transactions on Mathematical Software (TOMS)
The university of Florida sparse matrix collection

ACM Transactions on Mathematical Software (TOMS)

Quantified Score

Hi-index	0.00

Visualization

Abstract

One possible approach to the solution of large sparse linear systems is to reorder the system matrix to bordered block diagonal form and then to solve the block system in parallel. We consider the duality between singly bordered and doubly bordered block diagonal forms. The idea of a stabilized doubly bordered block diagonal form is introduced. We show how a stable factorization of a singly bordered block diagonal matrix results in a stabilized doubly bordered block diagonal matrix. We propose using matrix stretching to generate a singly bordered form from a doubly bordered form. Matrix stretching is compared with two alternative methods for obtaining a singly bordered form and is shown to be efficient both in computation time and the quality of the resulting block structure.