A collection of examples where Neville elimination outperforms Gaussian elimination

Alonso, Pedro; Delgado, Jorge; Gallego, Rafael; Peña, J. M.

doi:10.1016/j.amc.2010.03.094

Cited by 7 publications

(19 citation statements)

References 26 publications

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“…• If ε 2 (A) = −1, then A (1) = P n A (1) = P n A, and by Corollary 1 A (1) is ASSR with ε 2 (A (1) ) = 1. Besides, the first step of NE of this matrix can be performed without rows exchanges.…”

Section: Ne Two-determinant Pivoting and Auxiliary Resultsmentioning

confidence: 95%

“…• If ε 2 (A) = 1, then the first step of NE is performed without rows exchanges. In addition, A = A (1) = A (1) , and A (1) is ASSR with ε 2 (A (1) ) = 1.…”

Section: Ne Two-determinant Pivoting and Auxiliary Resultsmentioning

confidence: 99%

“…For this purpose, we analyze the entries of the matrix for testing whether it is type-I or type-II staircase. Let us consider the index i 1 of the zero pattern of A (1) . This index indicates the row in which appears the first zero in the first column of A (1) .…”

Section: Preservation Of Assr Matrices Through Ne Two-determinant Pivmentioning

confidence: 99%

“…Let us consider the index i 1 of the zero pattern of A (1) . This index indicates the row in which appears the first zero in the first column of A (1) . If the first column of A (1) does not contain zero elements, then i 1 = n + 1.…”

Section: Preservation Of Assr Matrices Through Ne Two-determinant Pivmentioning

confidence: 99%

“…Roughly speaking, NE consists of making zeros in a column of a matrix by adding to each row an adequate multiple of the previous one, instead of using just a row with a fixed pivot as in Gaussian elimination. Other advantages of NE can be seen in [1,12,13].…”

Section: Introductionmentioning

confidence: 99%

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Almost strictly sign regular matrices and Neville elimination with two-determinant pivoting

Alonso

Peña

Serrano

2016

Applied Mathematics and Computation

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In 2007 Cortés and Peña introduced a pivoting strategy for the Neville elimination of nonsingular sign regular matrices and called it two-determinant pivoting. Neville elimination has been very useful for obtaining theoretical and practical properties for totally positive (negative) matrices and other related types of matrices. A real matrix is said to be almost strictly sign regular if all its nontrivial minors of the same order have the same strict sign. In this paper, some nice properties related with the application of Neville elimination with two-determinant pivoting strategy to almost strictly sign regular matrices are presented.

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Section: Ne Two-determinant Pivoting and Auxiliary Resultsmentioning

confidence: 95%

“…• If ε 2 (A) = 1, then the first step of NE is performed without rows exchanges. In addition, A = A (1) = A (1) , and A (1) is ASSR with ε 2 (A (1) ) = 1.…”

Section: Ne Two-determinant Pivoting and Auxiliary Resultsmentioning

confidence: 99%