On the Solution of Singular Systems by Krylov Subspace Methods

摘要：

Krylov subspace methods are popular iterative methods to solve large sparse linear systems in the real-world computations due to their cheap memory requirement and computational cost. In this paper, we discuss the solution of singular systems. We will show that the consistency of a singular linear system is not a sufficient condition for a Krylov subspace method to successfully find a solution to the system. The choice of initial guess is a crucial step. If the initial guess is properly chosen, a Krylov method almost surely converges to find a solution from the point of view of probability, otherwise a Krylov subspace method surely diverges. Moreover, our algorithm applied to parallel calculation is discussed in the paper.

关键词： ML(n)BiCG multiple starting Lanczos Krylov subspace iterative methods linear systems

作者: Man-Chung Yeung

作者单位: Department of Mathematics University of Wyoming Wyoming, U.S.A.

会议类型: 国际会议

会议名称: 电子商务、工程及科学领域的分布计算和应用国际会议(DCABES 2010)

会议地点: 香港

会议语种:英文

页码: 620-622

在线出版日期: 2010-08-10（万方平台首次上网日期，不代表论文的发表时间）