New upper bounds for ∥ A − 1 ∥ ∞ of strictly diagonally dominant M-matrices

Wang, Feng; Sun, Defeng; Zhao, Jianxing

doi:10.1186/s13660-015-0696-2

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A Chain Condition1

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Cited by 4 publications

(3 citation statements)

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“…For certain specific constants ! ij ; i; j D 1; 2; : : : ; n, Wang, Sun and Zhao (Theorem 2, [137]) have shown that…”

Section: A Chain Conditionmentioning

confidence: 99%

Infinite Matrices and Their Recent Applications

Shivakumar¹,

Sivakumar²,

Zhang³

2016

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“…For certain specific constants ! ij ; i; j D 1; 2; : : : ; n, Wang, Sun and Zhao (Theorem 2, [137]) have shown that…”

Section: A Chain Conditionmentioning

confidence: 99%

Infinite Matrices and Their Recent Applications

Shivakumar¹,

Sivakumar²,

Zhang³

2016

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“…Various authors have recently studied the family of w.c.d.d. M-matrices, obtaining bounds on the infinity norm of their inverses (i.e., A −1 ∞ ) [19,5,14,23,10]. While a w.c.d.d.…”

Section: Introductionmentioning

confidence: 99%

A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix

Azimzadeh

2018

Math. Comp.

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We present a test for determining if a substochastic matrix is convergent. By establishing a duality between weakly chained diagonally dominant (w.c.d.d.) Lmatrices and convergent substochastic matrices, we show that this test can be trivially extended to determine whether a weakly diagonally dominant (w.d.d.) matrix is a nonsingular M-matrix. The test's runtime is linear in the order of the input matrix if it is sparse and quadratic if it is dense. This is a partial strengthening of the cubic test in [J. M. Peña., A stable test to check if a matrix is a nonsingular M-matrix, Math. Comp., 247, 1385-1392, 2004. As a by-product of our analysis, we prove that a nonsingular w.d.d. M-matrix is a w.c.d.d. L-matrix, a fact whose converse has been known since at least 1964. We point out that this strengthens some recent results on M-matrices in the literature.

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“…But it is difficult to determine nonsingular H − matrices in practice. The problem is investigated in some papers, (see [3][4][5][6][7][8][9][10][11]). In this paper, we obtain a practical criterion of H − matrices.…”

Section: Introductionmentioning

confidence: 99%

Criteria for <i>α</i>-Diagonally Dominant Matrices and its Applications

Chen

Min

2013

AMM

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How to check if a given matrix is a nonsingular matrix is important. In the recent paper, several simple criteria, as well as a necessary condition for nonsingular matrices, have been obtained. Inspired by these results, we partition the row and column index set of square matrix, construct a positive diagonal matrix according to the elements and row sum, column sum of the matrix as well, then obtain a new criterion for the nonsingular matrices, and extend the criteria of nonsingular matrices. Finally, a numerical example for the effectiveness of the proposed criterion is presented.

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New upper bounds for ∥ A − 1 ∥ ∞ of strictly diagonally dominant M-matrices

Cited by 4 publications

References 5 publications

Infinite Matrices and Their Recent Applications

Infinite Matrices and Their Recent Applications

A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix

Criteria for <i>α</i>-Diagonally Dominant Matrices and its Applications

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