Journal Article10.1142/S0129053389000056
Solving sparse triangular linear systems on parallel computers
Edward E. Anderson,Yousef Saad +1 more
182
TL;DR: This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations and considers both row-wise and jagged diagonal storage for the offdiagonal blocks.
read more
Abstract: This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. The second approach is to use a variable blocksize and reorder the unknowns so that the diagonal blocks are diagonal matrices. The latter technique is called level scheduling because of how it is represented in the adjacency graph, and both row-wise and jagged diagonal storage for the off-diagonal blocks are considered. These techniques are analyzed for general parallel computers and experiments are presented for the eight-processor Alliant FX/8.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
ILUT: A dual threshold incomplete LU factorization
TL;DR: This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in, and is a compromise between these two extremes.
755
Scan primitives for GPU computing
Shubhabrata Sengupta,Mark J. Harris,Yao Zhang,John D. Owens +3 more
- 04 Aug 2007
TL;DR: Using the scan primitives, this work shows novel GPU implementations of quicksort and sparse matrix-vector multiply, and analyzes the performance of the scanPrimitives, several sort algorithms that use the scan Primitives, and a graphical shallow-water fluid simulation using the scan framework for a tridiagonal matrix solver.
Iterative solution of linear systems in the 20th century
TL;DR: In this article, the main research developments in the area of iterative methods for solving linear systems during the 20th century are described and compared, and the most signicant contributions during the past century are compared to one another.
530
A survey of direct methods for sparse linear systems
TL;DR: The goal of this survey article is to impart a working knowledge of the underlying theory and practice of sparse direct methods for solving linear systems and least-squares problems, and to provide an overview of the algorithms, data structures, and software available to solve these problems.
254
Run-time parallelization and scheduling of loops
D. Baxter,Ravi Mirchandaney,Joel H. Saltz +2 more
- 01 Mar 1989
TL;DR: The authors have reached the conclusion that for the types of workloads they have investigated, self-execution almost always performs better than pre-scheduling and the improvement in performance that accrues as a result of global topological sorting of indices as opposed to the less expensive local sorting, is not very significant in the case of self-Execution.