论文标题
通过理性的Krylov子空间法解决对称和积极的确定二阶线性互补问题
Solving Symmetric and Positive Definite Second-Order Cone Linear Complementarity Problem by A Rational Krylov Subspace Method
论文作者
论文摘要
二阶线性互补问题（SOCLCP）是经典线性互补问题的概括。众所周知，具有全球唯一可解决的特性的SOCLCP基本上等同于一个零发现的问题，在该问题中，相关函数与模型降低中的传输函数具有很大相似之处[{\ em siam J. Sci。 Comput。}，37（2015），pp。〜A2046-A2075]。在本文中，我们提出了一种新的理性Krylov子空间方法，以解决对称和积极确定的SOCLCP的零找到问题。该算法由两个阶段组成：首先，它依赖于扩展的Krylov子空间来获得零根的粗糙近似值，然后应用多极有理的Krylov子空间投影迭代地迭代地获取准确的解决方案。对各种类型的SOCLCP示例的数值评估证明了其效率和鲁棒性。
The second-order cone linear complementarity problem (SOCLCP) is a generalization of the classical linear complementarity problem. It has been known that SOCLCP, with the globally uniquely solvable property, is essentially equivalent to a zero-finding problem in which the associated function bears much similarity to the transfer function in model reduction [{\em SIAM J. Sci. Comput.}, 37 (2015), pp.~A2046--A2075]. In this paper, we propose a new rational Krylov subspace method to solve the zero-finding problem for the symmetric and positive definite SOCLCP. The algorithm consists of two stages: first, it relies on an extended Krylov subspace to obtain rough approximations of the zero root, and then applies multiple-pole rational Krylov subspace projections iteratively to acquire an accurate solution. Numerical evaluations on various types of SOCLCP examples demonstrate its efficiency and robustness.
