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
收藏
页码：2238 / 2257
页数：20
相关论文
共 50 条
  • [31] Convergence rates for inverse-free rational approximation of matrix functions
    Jagels, Carl
    Mach, Thomas
    Reichel, Lothar
    Vandebril, Raf
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 510 : 291 - 310
  • [32] VLSI DESIGN OF INVERSE-FREE BERLEKAMP-MASSEY ALGORITHM
    REED, IS
    SHIH, MT
    TRUONG, TK
    IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES, 1991, 138 (05): : 295 - 298
  • [33] A MODIFIED INVERSE-FREE DYNAMICAL SYSTEM FOR ABSOLUTE VALUE EQUATIONS
    Han, Xin
    He, Xing
    Chen, Jiawei
    Ju, Xingxing
    JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2023, 7 (06): : 909 - 923
  • [34] Inverse-free recursive multiresolution algorithms for a data approximation problem
    Fortes, M. A.
    Raydan, M.
    Sajo-Castelli, A. M.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (04) : 1177 - 1187
  • [35] An inverse-free ADI algorithm for computing Lagrangian invariant subspaces
    Mehrmann, Volker
    Poloni, Federico
    NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2016, 23 (01) : 147 - 168
  • [36] Fast Inverse-Free Generalized Sparse Bayesian Learning Algorithm
    Liu, Xingchuan
    Han, Lin
    Zhu, Jiang
    Xu, Zhiwei
    2020 5TH INTERNATIONAL CONFERENCE ON COMPUTER AND COMMUNICATION SYSTEMS (ICCCS 2020), 2020, : 82 - 86
  • [37] An Inverse-Free Single-Keyed Tweakable Enciphering Scheme
    Bhaumik, Ritam
    Nandi, Mridul
    ADVANCES IN CRYPTOLOGY - ASIACRYPT 2015, PT II, 2015, 9453 : 159 - 180
  • [38] AN INERTIAL INVERSE-FREE DYNAMICAL SYSTEM FOR SOLVING ABSOLUTE VALUE EQUATIONS
    Yu, Dongmei
    Chen, Cairong
    Yang, Yinong
    Han, Deren
    JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2023, 19 (04) : 2549 - 2559
  • [39] Micro-Doppler frequency estimation and association via the inverse-free complex SBL TVAR method
    Su, Nan
    Dai, Fengzhou
    Liu, Hongwei
    Zhang, Bo
    IET RADAR SONAR AND NAVIGATION, 2021, 15 (10): : 1247 - 1265
  • [40] Growing Echo State Network With an Inverse-Free Weight Update Strategy
    Chen, Xiufang
    Luo, Xin
    Jin, Long
    Li, Shuai
    Liu, Mei
    IEEE TRANSACTIONS ON CYBERNETICS, 2023, 53 (02) : 753 - 764
12345