An infinity norm bound for the inverse of Dashnic–Zusmanovich type matrices with applications

Li, Chaoqian; Cvetković, Ljiljana; Wei, Yimin; Zhao, Jianxing

doi:10.1016/j.laa.2018.12.013

Cited by 30 publications

(15 citation statements)

References 43 publications

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“…Some upper bounds were proposed for A −1 ∞ and A −1 1 ; see [24,26,35,48]. As Theorem 7 holds for any scaling p-norm, it would be advantageous to use these norms.…”

Section: Condition Number Of Ave For ∞-Normmentioning

confidence: 99%

Error bounds and a condition number for the absolute value equations

Zamani

Milan

2022

Math. Program.

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Due to their relation to the linear complementarity problem, absolute value equations have been intensively studied recently. In this paper, we present error bound conditions for absolute value equations. Along with the error bounds, we introduce a condition number. We consider general scaled matrix p-norms, as well as particular p-norms. We discuss basic properties of the condition number, including its computational complexity. We present various bounds on the condition number, and we give exact formulae for special classes of matrices. Moreover, we consider matrices that appear based on the transformation from the linear complementarity problem. Finally, we apply the error bound to convergence analysis of two methods for solving absolute value equations.

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“…Some upper bounds were proposed for A −1 ∞ and A −1 1 ; see [24,26,35,48]. As Theorem 7 holds for any scaling p-norm, it would be advantageous to use these norms.…”

Section: Condition Number Of Ave For ∞-Normmentioning

confidence: 99%

Error bounds and a condition number for the absolute value equations

Zamani

Milan

2022

Math. Program.

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“…Condition number of AVE for ∞-norm. Some upper bounds were proposed for A −1 ∞ and A −1 1 ; see [23,25,31,40]. As Theorem 2.1 holds for any scaling p-norm, it would be advantageous to use these norms.…”

Section: 2mentioning

confidence: 99%

Error bounds and a condition number for the absolute value equations

Zamani¹,

Milan²

2019

Preprint

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Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute value equations. Along with the error bounds, we introduce an appropriate condition number. We consider general scaled matrix p-norms, as well as particular p-norms. We discuss basic properties of the condition number, its computational complexity, its bounds and also exact values for special classes of matrices. We consider also matrices that appear based on the transformation from the linear complementarity problem.

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“…It is well known that H-matrices are widely used in many subjects such as numerical algebra, the control system, mathematical physics, economics, and dynamical system theory [1,2,4,20]. An important problem among them is to find upper bounds for the infinity norm of the inverse of H-matrices, because it can be used to the convergence analysis of matrix splitting and matrix multi-splitting iterative methods for solving large sparse systems of linear equations [18], as well as linear complementarity problems [10][11][12][13]19]. For example, when solving linear systems in practice, it is important to have an economical method for estimating the condition number κ(A) of the matrix of coefficients, which shows how 'ill' the systems could be.…”

Section: Introductionmentioning

confidence: 99%

“…Bound (1) is usually called Varah's bound and works only for SDD matrices. Moreover, when the class of involved matrices is a wider subclass of H-matrices, such as doubly strictly diagonally dominant (DSDD) matrices, S-SDD matrices, weakly chained diagonally dominant matrices, Nekrasov matrices, S-Nekrasov matrices, and DZ-type matrices, upper bounds for A -1 ∞ are derived, which sometimes are tighter in the SDD case, see [3,5,7,9,10,15,16,21] and the references therein. Recently, Cvetković et al [6] presented two upper bounds for A -1 ∞ involved with {P 1 , P 2 }-Nekrasov matrices, which are only dependent on the entries of the matrix A.…”

Section: Introductionmentioning

confidence: 99%