具有张量积结构的绝对值方程:唯一可解性和数值解

Pub Date : 2022-06-10 DOI:10.21136/AM.2022.0169-21

Somayeh Mollahsani, Fatemeh Panjeh Ali Beik

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引用次数: 1

摘要

考虑具有一定张量积结构的绝对值方程。详细讨论了这类方程的两个方面:可解性和近似解。更确切地说，首先，给出了该类方程唯一可解的几个充分条件。在此基础上，构造了一种新的求解AVEs的迭代方法，并研究了该方法的收敛性。数值验证了所建立理论结果的有效性和所提出迭代方案的性能。

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Absolute Value Equations with Tensor Product Structure: Unique Solvability and Numerical Solution

We consider the absolute value equations (AVEs) with a certain tensor product structure. Two aspects of this kind of AVEs are discussed in detail: the solvability and approximate solution. More precisely, first, some sufficient conditions are provided which guarantee the unique solvability of this kind of AVEs. Furthermore, a new iterative method is constructed for solving AVEs and its convergence properties are investigated. The validity of established theoretical results and performance of the proposed iterative scheme are examined numerically.

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