Stability Anomalies of Some Jacobian-Free Iterative Methods of High Order of Convergence

被引：0

作者：

Cordero, Alicia ^{[1
]}

Maimo, Javier G. ^{[2
]}

Torregrosa, Juan R. ^{[1
]}

Vassileva, Maria P. ^{[2
]}

机构：

[1] Univ Politecn Valencia, Inst Univ Matemat Multidisciplinar, Camino Vera S-N, E-46022 Valencia, Spain

[2] Inst Tecnol Santo Domingo, Avda Proceres 49, Santo Domingo 10602, Dominican Rep

来源：

AXIOMS | 2019年 / 8卷 / 02期

关键词：

nonlinear systems; real multidimensional dynamics; stability; SOLVING SYSTEMS; NEWTON METHOD; FAMILY;

D O I：

10.3390/axioms8020051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this manuscript, we design two classes of parametric iterative schemes to solve nonlinear problems that do not need to evaluate Jacobian matrices and need to solve three linear systems per iteration with the same divided difference operator as the coefficient matrix. The stability performance of the classes is analyzed on a quadratic polynomial system, and it is shown that for many values of the parameter, only convergence to the roots of the problem exists. Finally, we check the performance of these methods on some test problems to confirm the theoretical results.

引用

页数：15

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