| 一族解非线性方程组的Broyden—ABS算法 |
| |
| 引用本文： | 葛仁东. 一族解非线性方程组的Broyden—ABS算法[J]. 大连民族学院学报, 2000, 2(1): 1-8 |
| |
| 作者姓名： | 葛仁东 |
| |
| 作者单位： | 大连民族学院基础部，辽宁大连开发区116600 |
| |
| 摘 要： | 提出了一族Broyden-ABS型算法，它的Jocobian矩阵是由一系列Boroyden的行递推所形成。它是把Broyden算法和ABS投影算法结合在一起，避免了在算法中求Jacobian矩阵F’（x）。同时避免了在算法中求差商带来的不稳定性。（见[5],[6]）。第二部分在标准假定下证明了所提出的算法具有超线性收敛。第三部分讨论了参数zj^(k),wj^(k)的选择。该算法具有很高的实用性。
|
| 关 键 词： | Broyden－ABS算法 非线性方程组 拟牛顿法 Broydon方法 ABS投影算法 Jacobian矩阵 超线性收敛 |
A Family of Broyden-ABS Type Methods for Solving Nonlinear System |
| |
| GE Ren-dong. A Family of Broyden-ABS Type Methods for Solving Nonlinear System[J]. Journal of Dalian Nationalities University, 2000, 2(1): 1-8 |
| |
| Authors: | GE Ren-dong |
| |
| Abstract: | This paper presents a family of Broyden-ABS algorithms, where the Jacobian is evaluated by a variation of Broyden's formula. The algorithm is similar, but differing in the definition of the vectors used in the update, from methods recently proposed by Huang and Galantai. Superlinear convergence is proved under standard assumptions. |
| |
| Keywords: | Nonlinear systems of equations quasi-NeWton methods Broyden method ABS algorithm Jacobian matrix. |
| 本文献已被 CNKI 维普 等数据库收录！ |
