Generalizing the LINPACK Condition Estimator

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Two generalizations of the Cline-Moler-Stewart-Wilkinson "LINPACK" condition estimator are described. One generalization combines the LINPACK notion of "look-ahead" with a new feature called "look-behind" that results in a more flexibly chosen right-hand side. The other generalization is a "divide-and-conquer" scheme that involves estimating the condition of certain principal submatrices whose dimension repeatedly doubles. Both generalizations require that maximization of simple objective functions. When seeking an L1 condition estimate, these functions are convex while inthe L2 case they are quadratic. All the algorithms considered appear to be at least as reliable as the LINPACK estimator and are equally efficient.

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1981-06
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Cornell University
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computer science; technical report
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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR81-462
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technical report
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