A New Iterative Solution Method for Solving Multiple Linear Systems

• 作者: Saeed Karimi
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: ITERATIVE METHOD MULTIPLE Linear Systems LSQR METHOD GL-LSQR METHOD PROJECTION METHOD
• 年，卷（期）: 2012,（3）
• 页码范围: 25-30
• 页数: 6页
• 分类号: O1

摘要

In this paper, a new iterative solution method is proposed for solving multiple linear systems A(i)x(i)=b(i), for 1≤ i ≤ s, where the coefficient matrices A(i) and the right-hand sides b(i) are arbitrary in general. The proposed method is based on the global least squares (GL-LSQR) method. A linear operator is defined to connect all the linear systems together. To approximate all numerical solutions of the multiple linear systems simultaneously, the GL-LSQR method is applied for the operator and the approximate solutions are obtained recursively. The presented method is compared with the well-known LSQR method. Finally, numerical experiments on test matrices are presented to show the efficiency of the new method.