Title

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.

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