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Interval algorithm for absolute value equations

100%
Wang A., Wang H., Deng Y.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1171-1184
EN
We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.
2
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A convergence analysis of SOR iterative methods for linear systems with weakH-matrices

76%
Zhang C.-y., Xue Z., Luo S.
Open Mathematics
|
2016
|
tom 14
|
nr 1
747-760
EN
It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
3
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Some new bounds of the minimum eigenvalue for the Hadamard product of anM-matrix and an inverseM-matrix

76%
Zhao J., Sang C.
Open Mathematics
|
2016
|
tom 14
|
nr 1
81-88
EN
Some convergent sequences of the lower bounds of the minimum eigenvalue for the Hadamard product of a nonsingular M-matrix B and the inverse of a nonsingular M-matrix A are given by using Brauer’s theorem. It is proved that these sequences are monotone increasing, and numerical examples are given to show that these sequences could reach the true value of the minimum eigenvalue in some cases. These results in this paper improve some known results.
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