A globally optimal iterative algorithm to solve an ill-posed linear system

被引：0

作者：

Liu, Chein-Shan ^{[1
]}

机构：

[1] Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

来源：

CMES - Computer Modeling in Engineering and Sciences | 2012年 / 84卷 / 04期

关键词：

Iterative methods - Vector spaces;

D O I：

暂无

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学科分类号：

摘要：

An iterative algorithm based on the critical descent vector is proposed to solve an ill-posed linear system: Bx = b. We define a future cone in the Minkowski space as an invariant manifold, wherein the discrete dynamics evolves. A critical value ac in the critical descent vector u =αcr+BTr is derived, which renders the largest convergence rate as to be the globally optimal iterative algorithm (GOIA) among all the numerically iterative algorithms with the descent vector having the form u =αr+BTr to solve the ill-posed linear problems. Some numerical examples are used to reveal the superior performance of the GOIA. Copyright © 2012 Tech Science Press.

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页码：383 / 403