INVERSE-FREE NEWTON'S METHOD

被引：0

作者：

Massalski, Marcin ^{[1
]}

Nockowska-Rosiak, Magdalena ^{[1
]}

机构：

[1] Lodz Univ Technol, Inst Math, al Politech 8, PL-93590 Lodz, Poland

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2025年 / 15卷 / 04期

关键词：

Newton's method; at least quadratic convergence; approximate inverse; NONLINEAR EQUATIONS; ITERATIVE METHOD; MATRIX;

D O I：

10.11948/20240428

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a modification of Newton's method for finding a zero of a multivariable function without an inverse of a matrix in a recurrence. The aim of this paper is twofold: demonstrating at least quadratic convergence of a Newton-type method avoiding matrix inversion under standard assumptions, and then comparing modified and classical Newton's methods numerically.

引用

页码：2238 / 2257

页数：20

共 35 条

[1] Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations
Argyros, Ioannis K.
George, Santhosh
Regmi, Samundra
Argyros, Christopher I.
[J]. ALGORITHMS, 2024, 17 (04)
[2] Asymptotically Newton-Type Methods without Inverses for Solving Equations
Argyros, Ioannis K.
George, Santhosh
Shakhno, Stepan
Regmi, Samundra
Havdiak, Mykhailo
Argyros, Michael I.
[J]. MATHEMATICS, 2024, 12 (07)
[3] Newton's Method Without Division
Blanchard, Jeffrey D.
Chamberland, Marc
[J]. AMERICAN MATHEMATICAL MONTHLY, 2023, 130 (07) : 606 - 617
[4] Bohner M., 2001, DYNAMIC EQUATIONS TI, DOI DOI 10.1007/978-1-4612-0201-1
[5] BROYDEN CG, 1965, MATH COMPUT, V19, P557
[6] Iterative methods improving Newton's method by the decomposition method
Chun, C
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 50 (10-12) : 1559 - 1568
[7] Variants of Newton's Method using fifth-order quadrature formulas
Cordero, A.
Torregrosa, Juan R.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (01) : 686 - 698
[8] NEWTON-ANDERSON AT SINGULAR POINTS
Dallas, Matt
Pollock, Sara
[J]. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2023, 20 (05) : 667 - 692
[9] EXPANDED CONVERGENCE DOMAINS FOR NEWTON METHOD AT NEARLY SINGULAR ROOTS
DECKER, DW
KELLEY, CT
[J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1985, 6 (04): : 951 - 966
[10] ON SOLVING NONLINEAR EQUATIONS WITH SIMPLE SINGULARITIES OR NEARLY SINGULAR SOLUTIONS
GRIEWANK, A
[J]. SIAM REVIEW, 1985, 27 (04) : 537 - 563

← 1 2 3 4 →