Improving an estimate of the convergence rate of the seidel method by selecting the optimal order of equations in the system of linear algebraic equations

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• 作者：A. N. Borzykh
• 关键词：Seidel method ; one ; step cyclic process ; system of linear algebraic equations ; iterative methods for solving SLAEs ; convergence of the Seidel method ; estimate of the convergence rate of the Seidel method
• 刊名：Computational Mathematics and Mathematical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：57
• 期：1
• 页码：1-6
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Computational Mathematics and Numerical Analysis;
• 出版者：Pleiades Publishing
• ISSN：1555-6662
• 卷排序：57

文摘

The Seidel method for solving a system of linear algebraic equations and an estimate of its convergence rate are considered. It is proposed to change the order of equations. It is shown that the method described in Faddeevs’ book Computational Methods of Linear Algebra can deteriorate the convergence rate estimate rather than improve it. An algorithm for establishing the optimal order of equations is proposed, and its validity is proved. It is shown that the computational complexity of the reordering is 2n2 additions and (12)n2 divisions. Numerical results for random matrices of order 100 are presented that confirm the proposed improvement.