A Comparison of Pivoting Strategies for the Direct LU Factorization

Oliver Y. Chen

Department of Mathematics
Montana State Univesity - Billings
Billings, MT 59101-0298
USA
Phone: (406) 657-2969
Fax: (406) 657-2037
cs_chen@vesper.emcmt.edu

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ABSTRACT

We combine the idea of the direct LU factorization with the idea of the pivoting strategy in the usual Gaussian elimination and show that two so-called total scaled and total pivoting strategies can be employed in addition to the traditional pivoting strategies: partial scaled, partial, and direct diagonal. In this paper we offer a general LU factorization with total scaled pivoting algorithm from which the other well-known pivoting and non-pivoting algorithms can be driven. We utilize the random number routines in MSU-Billings' main frame computer to compare these pivoting strategies and conclude that none of the five strategies is absolutely more accurate than the other but generally their accuracy descending order is the same as their appearing order in the above.

Keyword(s): linear algebra, numerical methods