Improved form of the conjugate gradient method

被引：0
|
作者：
Kalitkin N.N. [1 ]
Kuz’mina L.V. [1 ]
机构：
[1] Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow
来源：
Mathematical Models and Computer Simulations | 2012年 / 4卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
conditioning; conjugate gradient method; preconditioner; rounding errors; systems of linear algebraic equations;
D O I：
10.1134/S2070048212010061
中图分类号：
学科分类号：
摘要：
The conjugate gradient method, which is used for solving systems of linear algebraic equations, is studied. A notation for the method has been found, which proved to be the simplest and the most resistant to rounding errors. A criterion is constructed for the end of iterations based on the prevalence of rounding errors. Numerical calculations are made illustrating the specifics of the method convergence for well- and ill-posed problems. The generalization of this form is written for problems with preconditioning. © 2012, Pleiades Publishing, Ltd.
引用
收藏
页码：68 / 81
页数：13
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