A Geometric Analysis of Gaussian Elimination. II
Document Type
Article
Publication Date
1-1-1992
Description
In Part I of this work, we began a discussion of the numeric consequences of hyperplane orientation in Gaussian elimination. We continue this discussion by introducing the concept of back-substitution-phase error multipliers. These error multipliers help to explain many of the previously unproven or poorly understood observations concerning Gaussian elimination in a finite-precision environment. A new pivoting strategy designed to control both sweepout phase roundoff error and back-substitution-phase instability is also presented. This new strategy, called rook's pivoting, is only slightly more expensive than partial pivoting yet produces results comparable to those produced by complete pivoting.
Citation Information
Neal, Larry; and Poole, George. 1992. A Geometric Analysis of Gaussian Elimination. II. Linear Algebra and Its Applications. Vol.173(C). 239-264. https://doi.org/10.1016/0024-3795(92)90432-A ISSN: 0024-3795