Symbolic and Exact Structure Prediction for Sparse Gaussian Elimination with Partial Pivoting

2009 ◽  
Vol 30 (4) ◽  
pp. 1520-1545 ◽  
Author(s):  
Laura Grigori ◽  
John R. Gilbert ◽  
Michel Cosnard
Keyword(s):  
Structure Prediction ◽  
Gaussian Elimination ◽  
Partial Pivoting

scholarly journals Scientific Programming with High Performance Fortran: A Case Study Using the xHPF Compiler

1997 ◽  
Vol 6 (1) ◽  
pp. 127-152
Author(s):  
Eric De Sturler ◽  
Volker Strumpen
Keyword(s):  
High Performance ◽  
Parallel Implementation ◽  
Gaussian Elimination ◽  
Primary Objective ◽  
Matrix Product ◽  
Dense Matrix ◽  
High Performance Fortran ◽  
Partial Pivoting ◽  
Intel Paragon

Recently, the first commercial High Performance Fortran (HPF) subset compilers have appeared. This article reports on our experiences with the xHPF compiler of Applied Parallel Research, version 1.2, for the Intel Paragon. At this stage, we do not expect very High Performance from our HPF programs, even though performance will eventually be of paramount importance for the acceptance of HPF. Instead, our primary objective is to study how to convert large Fortran 77 (F77) programs to HPF such that the compiler generates reasonably efficient parallel code. We report on a case study that identifies several problems when parallelizing code with HPF; most of these problems affect current HPF compiler technology in general, although some are specific for the xHPF compiler. We discuss our solutions from the perspective of the scientific programmer, and presenttiming results on the Intel Paragon. The case study comprises three programs of different complexity with respect to parallelization. We use the dense matrix-matrix product to show that the distribution of arrays and the order of nested loops significantly influence the performance of the parallel program. We use Gaussian elimination with partial pivoting to study the parallelization strategy of the compiler. There are various ways to structure this algorithm for a particular data distribution. This example shows how much effort may be demanded from the programmer to support the compiler in generating an efficient parallel implementation. Finally, we use a small application to show that the more complicated structure of a larger program may introduce problems for the parallelization, even though all subroutines of the application are easy to parallelize by themselves. The application consists of a finite volume discretization on a structured grid and a nested iterative solver. Our case study shows that it is possible to obtain reasonably efficient parallel programs with xHPF, although the compiler needs substantial support from the programmer.

Communication Efficient Gaussian Elimination with Partial Pivoting using a Shape Morphing Data Layout

2013 ◽  
Author(s):  
Grey Ballard ◽  
James Demmel ◽  
Benjamin Lipshitz ◽  
Oded Schwartz ◽  
Sivan Toledo
Keyword(s):  
Gaussian Elimination ◽  
Data Layout ◽  
Shape Morphing ◽  
Partial Pivoting

Systolic Gaussian elimination over GF(p) with partial pivoting

1989 ◽  
Vol 38 (9) ◽  
pp. 1321-1324 ◽  
Author(s):  
B. Hochet ◽  
P. Quinton ◽  
Y. Robert
Keyword(s):  
Gaussian Elimination ◽  
Partial Pivoting
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