An efficient approach for solving saddle point problems using block structure
An efficient approach for solving saddle point problems using block structure
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DOI：
10.15748/jasse.8.114
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发表时间：
2021
影响因子：
0.5
通讯作者：
Hiroto Tadano;Shota Ishikawa
中科院分区：
文献类型：
--
作者：
Hiroto Tadano;Shota Ishikawa
本文主要研究2 × 2块系数矩阵的鞍点问题。当系数矩阵的右上分块列数和左下分块行数较大时，即使左上分块是良条件矩阵，Krylov子空间方法求解鞍点问题的收敛性往往较差。本文提出了一种利用问题的块结构求解鞍点问题的有效方法。我们提出的方法中最耗时的部分是具有多个右侧的线性系统的解。为了有效地求解具有多个右手边的线性系统，我们提出将块Krylov子空间方法应用于该线性系统。数值实验表明，基于块Krylov子空间方法的鞍点问题求解在迭代次数和计算时间上都优于传统方法。
This paper focuses on saddle point problems with a 2-by-2 block coefficient matrix. When the number of columns in the upper-right block and the number of rows in the lower-left block of the coefficient matrix is large, the convergence behavior of Krylov subspace methods for the saddle point problems tends to be poor even if the upper-left block is a well-conditioned matrix. In this paper, an efficient approach for solving the saddle point problems using block structure of the problems is proposed. The most time-consuming part of our proposed approach is the solution of a linear system with multiple right-hand sides. To solve the linear system with multiple right-hand sides efficiently, we propose to apply Block Krylov subspace methods to this linear system. Numerical experiments show that the proposed approach with Block Krylov subspace methods can solve the saddle point problems more efficiently than the conventional approach in terms of the number of iterations and the computation time.