Almost strictly totally negative matrices: An algorithmic characterization

Alonso, Pedro; Peña, J. M.; Serrano, María Luisa

doi:10.1016/j.cam.2014.07.027

Cited by 5 publications

(7 citation statements)

References 23 publications

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“…given by the expression and conditions (2). Analogously, the TP matrix U admits the unique bidiagonal factorization,…”

Section: Are the Unit Lower (Upper) Bidiagonal Tp Matrices Defined Bymentioning

confidence: 99%

“…are unit lower (upper) bidiagonal TP matrices given by expressions (2) and (3), respectively, and satisfying the conditions β i,j > 0 and α i,j > 0, for all i = 1, 2, . .…”

Section: Corollary 1 Letmentioning

confidence: 99%

“…Recently, in [2] an algorithmic characterization of nonsingular almost strictly totally negative matrices is given through the Neville elimination. For t.n.p.…”

mentioning

confidence: 99%

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On the characterization of totally nonpositive matrices

Cantó

Peláez²,

Urbano

2016

SeMA

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A nonpositive real matrix A = (a ij ) 1≤i,j≤n is said to be totally nonpositive (negative) if all its minors are nonpositive (negative) and it is abbreviated as t.n.p. (t.n.). In this work a bidiagonal factorization of a nonsingular t.n.p. matrix A is computed and it is stored in an matrix represented by BD (t.n.p.) (A) when a 11 < 0 (or BD (zero) (A) when a 11 = 0). As a converse result, an efficient algorithm to know if an matrix BD (t.n.p.) (A) (BD (zero) (A)) is the bidiagonal factorization of a t.n.p. matrix with a 11 < 0 (a 11 = 0) is given. Similar results are obtained for t.n. matrices using the matrix BD (t.n.) (A), and these characterizations are extended to rectangular t.n.p. (t.n.) matrices. Finally, the bidiagonal factorization of the inverse of a nonsingular t.n.p. (t.n.) matrix A is directly obtained from BD (t.n.p.) (A) (BD (t.n.) (A)).

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“…given by the expression and conditions (2). Analogously, the TP matrix U admits the unique bidiagonal factorization,…”

Section: Are the Unit Lower (Upper) Bidiagonal Tp Matrices Defined Bymentioning

confidence: 99%

“…are unit lower (upper) bidiagonal TP matrices given by expressions (2) and (3), respectively, and satisfying the conditions β i,j > 0 and α i,j > 0, for all i = 1, 2, . .…”

Section: Corollary 1 Letmentioning

confidence: 99%

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On the characterization of totally nonpositive matrices

Cantó

Peláez²,

Urbano

2016

SeMA

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“…, −1). So, in [3] an algorithmic characterization of nonsingular ASTN matrices is presented. All nontrivial minors of these matrices are strictly negative, which notably simplifies the characterization proposed in [2] for ASSR matrices.…”

Section: Introductionmentioning

confidence: 99%

“…ASTN matrices contain all strictly totally negative matrices (which are matrices with all their minors negative) and are contained in the class of totally negative matrices (which are matrices with all their minors nonpositive). See [3,5,8,9,16] about these classes of matrices.…”

Section: Introductionmentioning

confidence: 99%

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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