新预条件Gauss-Seidel迭代法及收敛性比较

薄利艳; 杨晋

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新预条件Gauss-Seidel迭代法及收敛性比较

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- 新预条件Gauss-Seidel迭代法及收敛性比较
- 新预条件Gauss-Seidel迭代法及收敛性比较
- Issue 1, (2012)
- 作者机构：
  
  太原理工大学数学学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：2012
- 稿件说明：
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薄利艳, 杨晋. 新预条件Gauss-Seidel迭代法及收敛性比较[J]. 2012, (1).
DOI：

薄利艳, 杨晋. 新预条件Gauss-Seidel迭代法及收敛性比较[J]. 2012, (1). DOI：

摘要

针对Gauss-Seidel迭代法求解线性方程组

引入了一种新的预条件矩阵.当系数矩阵为广泛应用的M-矩阵时

给出了该预条件Gauss-Seidel迭代法与经典Gauss-Seidel迭代法的比较定理

其说明了新预条件Gauss-Seidel迭代法是收敛的且加速了经典Gauss-Seidel迭代法的收敛速率.证明了新预条件Gauss-Seidel迭代法优于已有预条件Gauss-Seidel迭代法.最后用一个数值例子来验证所得结论的有效性.

Abstract

A new preconditioned matrix was introduced for solving linear systems with Gauss-Seidel iterative method.Under the condition that the coefficient matrix being an M-matrix

which is widely used

the comparison theorem between preconditioned Gauss-Seidel iterative method and classic Gauss-Seidel iterative method was given.The preconditioned Gauss-Seidel iterative method is convergent and it accelerates the convergent speed of classic Gauss-Seidel iterative method.It showed that newly proposed preconditioned Gauss-Seidel iterative method is superior to the Gauss-Seidel iterative method mentioned.A numerical example was given to verify the effectiveness of the conclusions.

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