ON DOWNHILL METHOD

被引：36

作者：

BACH, H

机构：

[1] Technical Univ. of Denmark, Lyngby

来源：

COMMUNICATIONS OF THE ACM | 1969年 / 12卷 / 12期

关键词：

algebraic complex equation; complex equation; complex iteration; complex relaxation method; downhill method; transcendental complex equation;

D O I：

10.1145/363626.363636

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The downhill method is a numerical method for solving complex equations f(z) = 0 on which the only restriction is that the function w = f(z) must be analytical. An introduction to this method is given and a critical review of relating literature is presented. Although in theory the method always converges, it is shown that a fundamental dilemma exists which may cause a breakdown in practical applications. To avoid this difficulty and to improve the rate of convergence toward a root, some modifications of the original method are proposed and a program (FORTRAN) based on the modified method is given in Algorithm 365. Some numerical examples are included. © 1969 ACM. All rights reserved.

引用

页码：675 / &