Permuting Sparse Rectangular Matrices into Block-Diagonal Form

Permuting Sparse Square Matrices into Block Diagonal Form with Overlap

In this whitepaper, we describe the problem of permuting sparse square matrices into block diagonal form with overlap (BDO) and propose a graph partitioning algorithm for solving this problem. A block diagonal matrix with overlap is a block diagonal matrix whose consecutive diagonal blocks may overlap. The objective in this permutation problem is to minimize the total overlap size, whereas the ...

A Recursive Bipartitioning Algorithm for Permuting Sparse Square Matrices into Block Diagonal Form with Overlap

We investigate the problem of symmetrically permuting a square sparse matrix into a block diagonal form with overlap. This permutation problem arises in the parallelization of an explicit formulation of the multiplicative Schwarz preconditioner and a more recent block overlapping banded linear solver as well as its application to general sparse linear systems. In order to formulate this permuta...

Singly-Bordered Block-Diagonal Form for Minimal Problem Solvers

The Gröbner basis method for solving systems of polynomial equations became very popular in the computer vision community as it helps to find fast and numerically stable solutions to difficult problems. In this paper, we present a method that potentially significantly speeds up Gröbner basis solvers. We show that the elimination template matrices used in these solvers are usually quite sparse a...

oGPVS/BDO: A Software Package for Ordered Graph Partitioning by Vertex Separators and Permuting Matrices into Block Diagonal Form with Overlap

Parallel Block-Diagonal-Bordered Sparse Linear Solvers for Electrical Power System Applications

Research is ongoing that examines parallel direct block-diagonal-bordered sparse linear solvers for irregular sparse matrix problems derived from electrical power system applications. Parallel block-diagonal-bordered sparse linear solvers exhibit distinct advantages when compared to current general parallel direct sparse matrix solvers. Our research shows that actual power system matrices can b...