Comparing robust forms of iterative methods of conjugate directions

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• 作者：A. A. Belov ; N. N. Kalitkin ; L. V. Kuzmina
• 关键词：systems of linear algebraic equations ; sparse matrices ; iterative methods ; conjugate gradient descents
• 刊名：Mathematical Models and Computer Simulations
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：8
• 期：2
• 页码：155-174
• 全文大小：1,016 KB
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• 作者单位：A. A. Belov (1)
  N. N. Kalitkin (1)
  L. V. Kuzmina (1)
  
  1. Faculty of Physics, Moscow State University, Moscow, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Modeling and IndustrialMathematics
  Simulation and Modeling
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：2070-0490

文摘

Simple and robust formulas of the conjugate direction method for symmetric matrices and of the symmetrized conjugate gradient method for nonsymmetric matrices have been constructed. These methods were compared with robust forms of the conjugate gradient method and the Craig method using test problems. It is shown that stability for the round-off error can be attained when recurrent variants of the methods are used. The most reliable and efficient method for symmetric signdefinite and indefinite matrices appears to be the method of conjugate residuals. For nonsymmetric matrices, the best results have been obtained by the method of symmetrized conjugate gradients. These two methods are recommended for writing standard programs. A reliable criterion has also been constructed for the termination of the calculation on reaching background values due to the round-off errors.