| 求非线性方程组的数值解的MRV迭代法的特殊应用 |
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| 引用本文： | 刘长河,汪元伦.求非线性方程组的数值解的MRV迭代法的特殊应用[J].北京建筑工程学院学报,2006,22(3):58-60. |
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| 作者姓名： | 刘长河 汪元伦 |
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| 作者单位： | 北京建筑工程学院,基础科学部,北京,100044;绵阳师范学院数学与信息科学系,四川绵阳,621000 |
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| 摘 要： | MRV迭代法是求非线性方程组的数值解的一种Newton型迭代法.它通过修改右端向量,使得迭代过程中各步的线性方程组具有相同的系数矩阵.其收敛速度较快, 界于定点Newton法和Newton迭代法之间.借助于LU分解,可使其计算成本降低,低于定点Newton法.将MRV迭代法用于只含一个非线性方程的非线性方程组, 得到一种新的迭代法--SMRV迭代法.其计算成本更低,收敛速度更快.其收敛速度与Newton迭代法相同,即至少是平方收敛的.
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| 关 键 词： | 非线性方程组 数值解 Newton型迭代法 |
| 文章编号： | 1004-6011（2006）03-0058-03 |
| 收稿时间： | 2005-10-20 |
| 修稿时间： | 2005年10月20日 |
Application of MRV Iteration Method on Solving the Numerical Solution of one Kind of Special System of Non-linear Equations |
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| Liu Changhe,Wang Yuanlun.Application of MRV Iteration Method on Solving the Numerical Solution of one Kind of Special System of Non-linear Equations[J].Journal of Beijing Institute of Civil Engineering and Architecture,2006,22(3):58-60. |
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| Authors: | Liu Changhe Wang Yuanlun |
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| Affiliation: | 1. Dept. of Basic Scences, Beijing 100044; 2. Dept. of Information and Mathematics, Mianyang Normal College, Mianyang 621000 |
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| Abstract: | MRV iteration method is a Newton-like method for solving the numerical solution of non-linear system.By modifying the right-hand-side vector,the linear systems in each iterate have the same coefficient matrix.It converges faster than fixed Newton method and slower than Newton method.When LU decomposition method is used,its cost is less than that of Newton method.In this paper,a new iteration method,SMVR algorithm is proposed by performing MVR algorithm on a kind of special non-linear system,in which has only one non-linear equation.Except costs less,it converges the same fast as Newton method,i.e.,it is quadratic convergence. |
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| Keywords: | system of non-linear equations numerical solution newton-like iteration method |
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