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Sparse Partial Pivoting in Time Proportional to Arithmetic Operations

Author
Gilbert, John R.; Peierls, Timothy
Abstract
Existing sparse partial pivoting algorithms can spend asymptomatically more time manipulating data structures than doing arithmetic, although they are tuned to be efficient on many large problems. We present an algorithm to factor sparse matrices by Gaussian elimination with partial privoting in time proportional to the number of arithmetic operations. Implementing this algorithm requires only simple data structures and gives a code that is competitive with, and often faster than, existing sparse codes. The key idea is a new triangular solver that uses depth-first search and topological ordering to take advantage of sparsity in the right-hand side.
Date Issued
1986-09Publisher
Cornell University
Subject
computer science; technical report
Previously Published As
http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR86-783
Type
technical report