Pivoting to normalize a basic matrix

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1993 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Programming, volume 62, pages 553-556 (issn: 0025-5610, eissn: 1436-4646,

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Authors: B. Curtis Eaves;

doi: 10.1007/bf01585183

Pivoting to normalize a basic matrix

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Abstract

The author calls an \(m\times n\) matrix \(A\) basic if some \(m\times n\) submatrix of columns is a permutation matrix. Given such \(A\), he shows that by repeatedly pivoting on elements which exceed one in absolute value, one brings \(A\) into a basic form, where all elements have an absolute value of one or less. The algorithm resembles the simplex method.

Related Organizations

École Polytechnique
France
Stanford University
United States

Keywords

Numerical computation of matrix norms, conditioning, scaling, basic matrix, pivoting, Direct numerical methods for linear systems and matrix inversion, simplex method

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