An inverse-free dynamical system for solving the absolute value equations

Chen, Cairong; Yang, Yinong; Yu, Dongmei; Han, Deren

doi:10.1016/j.apnum.2021.06.002

Cited by 25 publications

(37 citation statements)

References 45 publications

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“…Without limiting the matrix type, some computable estimates for their upper bounds are given. These bounds are sharper than the existing bounds in [20] under certain conditions. Secondly, we establish the framework of perturbation bounds for the AVEs and present some computable upper bounds.…”

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confidence: 52%

“…Although the AVEs in [3] is a NP-hard problem, so far, a large number of theoretical results, numerical methods and applications have been extensively excavated. For instance, among the theoretical results, in spite of determining the existence of a solution to the AVEs in [5,20] is NP-hard, and checking whether the AVEs has unique or multiple solutions in [6] is also NP-complete, there still exist some very important conclusions, in particular, some sufficient and necessary conditions for ensuring the existence and uniqueness of the solutions of the AVEs (1.1), (1.2) and (1.3) were established for any b ∈ R n , see [2,[7][8][9].…”

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confidence: 99%

“…With respect to this regard, to our knowledge, the perturbation analysis of the AVEs (1.1) and (1.2) has not been discussed. In addition, for the error bound of AVEs, under the assumption of strongly monotone property, a global projection-type error bound was provided in [20]. Obviously, this kind of conditional projection-type error bound frequently has great limitation.…”

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confidence: 99%

“…In [20], with strongly monotone property, Chen et al also considered the global error bound of the AVEs (1.3) and presented the following result.…”

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confidence: 99%

“…Theorem 2.4. (Theorem 4.1 in [20]) Let x * be the unique solution of AVEs (1.3). Then for any x ∈ R n ,…”

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confidence: 99%

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The error bounds and perturbation bounds of the absolute value equations and some applications

Wu¹

2022

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In this paper, by introducing a class of absolute value functions, we study the error bounds and perturbation bounds of two types of absolute value equations (AVEs): Ax − B|x| = b and Ax − |Bx| = b. Some useful error bounds and perturbation bounds for the above two types of absolute value equations are presented. By applying the absolute value equations, we obtain some useful error bounds and perturbation bounds for the horizontal linear complementarity problem (HLCP). Incidentally, two new error bounds for linear complementarity problem (LCP) are given, coincidentally, which are equal to the existing result. Without constraint conditions, a new perturbation bound for the LCP is given as well. Besides, without limiting the matrix type, some computable estimates for the above upper bounds are given, which are sharper than some existing results under certain conditions. Some numerical examples for the AVEs from the LCP are given to show the feasibility of the perturbation bounds.

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confidence: 52%