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两种解非线性方程组的四阶迭代方法

  

  1. 合肥工业大学数学学院, 合肥 230009
  • 收稿日期:2011-09-06 出版日期:2012-06-15 发布日期:2012-06-13
  • 基金资助:
    国家自然科学基金资助项目(60773043, 61070227); 教育部科学技术研究重大项目(309017).

代璐璐,  檀结庆. 两种解非线性方程组的四阶迭代方法[J]. 数值计算与计算机应用, 2012, 33(2): 121-128.

Dai Lulu, Tan Jieqing. THE TWO KINDS OF ITERATIVE METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS WITH FOURTH-ORDER CONVERGENCE[J]. Journal of Numerical Methods and Computer Applications, 2012, 33(2): 121-128.

THE TWO KINDS OF ITERATIVE METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS WITH FOURTH-ORDER CONVERGENCE

Dai Lulu, Tan Jieqing   

  1. College of Mathematics, Hefei University of Technology, Hefei 230009, China
  • Received:2011-09-06 Online:2012-06-15 Published:2012-06-13
本文给出了两种新的解非线性方程组的迭代方法, 证明了它们具有四阶收敛性, 通过数值实例对几种不同的迭代方法和本文提出的两种新方法进行了分析比较, 说明了本文方法的有效性.
In this paper, we obtain two new iterative methods to solve systems of nonlinear equations, which are all based on quadrature formulas, and prove their convergence. Numerical examples are given to show that our methods, compared with other iterative methods, have a significant improvement.

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[1] 李庆扬, 莫孜中, 祁力群等. 非线性方程组的数值解法[M]. 北京: 科学出版社, 1987.
[2] 奥加特 J M, 莱因博尔特 W C. 多元非线性方程组迭代解法[M]. 北京: 科学出版社, 1983.
[3] 同济大学计算数学教研室编. 现代数值计算[M]. 北京: 人民邮电出版社, 2009.
[4] Frontini M, Sormani E. Third-order methods from quadrature formulae for solving systems of nonlinear equations[J]. Applied Mathematics and Computation, 2004, 149: 771-782.
[5] Muhammad Aslam Noor, Muhammad Waseem. Some iterative methods for solving a system of nonlinear Equations[J]. Computers and Mathematics with Applications, 2009, 57: 101-106.
[6] Darvishi M T, Barati A. A fourth-order method from quadrature formulae to solve systems of nonlinear equations[J]. Applied Mathematics and Computation, 2007, 188: 257-261.
[7] Maitree Podisuk, Ungsana Chundang, Wannaporn Sanprasert. Single step formulas and multi-step formulas of the integration method for solving the initial value problem of ordinary differential equation[J]. Applied Mathematics and Computation, 2007, 190: 1438-1444.
[8] Darvishi M T, Barati A. A third-order Newton-type method to solve systems of nonlinear equations[ J]. Applied Mathematics and Computation, 2007, 187: 630-635.
[9] Darvishi M T, Barati A. Super cubic iterative methods to solve systems of nonlinear Equations[J]. Applied Mathematics and Computation, 2007, 188: 1678-1685.
[10] Ortega J M, Rheinboldt W C. Iterative Solution of Nonlinear Equations in Several Variables[M]. Academic Press, New York and London, 1970.
[11] 杨柳, 陈艳萍. 一种新的Levenberg-Marquardt 算法的收敛性[J]. 计算数学, 2005, 27: 55-62.
[12] 杨柳, 陈艳萍. 求解非线性方程组的一种新的全局收敛的Levenberg-Marquardt 算法[J]. 计算数学, 2008, 30: 388-396.
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