On Growth in Gaussian Elimination with Complete Pivoting | Zendy

Nicholas I. M. Gould | Zendy

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On Growth in Gaussian Elimination with Complete Pivoting

Author(s) -

Nicholas I. M. Gould

Publication year - 1991

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/0612025

Subject(s) - gaussian elimination , mathematics , matrix (chemical analysis) , gaussian , combinatorics , algebra over a field , pure mathematics , computational chemistry , chemistry , materials science , composite material

It has been conjectured that when Gaussian elimination with complete pivoting is applied to a real n-by-n matrix, the maximum possible growth is n. In this note, a 13-by-13 matrix is given, for which the growth is 13.0205. The matrix was constructed by solving a large nonlinear programming problem. Growth larger than n has also been observed for matrices of orders 14, 15, and 16.

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