On an iterative algorithm of order 1.839... for solving the nonlinear least squares problems

被引：27
|
作者：
Shakhno, SM [1 ]
Gnatyshyn, OP [1 ]
机构：
[1] Ivan Franko Natl Univ Lviv, Dept Appl Math & Comp Sci, UA-79602 Lvov, Ukraine
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 161卷 / 01期
关键词：
nonlinear least squares problem; free-derivative iteration method; order convergence; residual;
D O I：
10.1016/j.amc.2003.12.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper for solving the nonlinear least-squares problem we propose new free-derivative iteration method with the order of convergence 1.839... We have elaborated the scheme of proof, by which from one point of view the theoretical research of one class of difference iterative methods with different orders of convergence have been conducted. By the results of numerical experiment, the new method is compared with the known difference methods and with the classic Gauss-Newton method. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：253 / 264
页数：12
相关论文
共 50 条
  • [41] ON SOLVING NONLINEAR LEAST-SQUARES PROBLEMS IN CASE OF RANK DEFICIENT JACOBIANS
    MENZEL, R
    COMPUTING, 1985, 34 (01) : 63 - 72
  • [42] Modified inexact Levenberg–Marquardt methods for solving nonlinear least squares problems
    Jifeng Bao
    Carisa Kwok Wai Yu
    Jinhua Wang
    Yaohua Hu
    Jen-Chih Yao
    Computational Optimization and Applications, 2019, 74 : 547 - 582
  • [43] An iterative algorithm for total least squares estimation
    Lu, Tieding
    Zhou, Shijian
    Wuhan Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University, 2010, 35 (11): : 1351 - 1354
  • [44] An efficient Gauss–Newton algorithm for solving regularized total least squares problems
    Hossein Zare
    Masoud Hajarian
    Numerical Algorithms, 2022, 89 : 1049 - 1073
  • [45] A SIMPLE ALGORITHM FOR LARGE, NONLINEAR OR SINGULAR LEAST-SQUARES PROBLEMS
    MYRHEIM, J
    RUE, H
    BUGGE, L
    NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 1993, 327 (2-3): : 539 - 543
  • [46] Parallel algorithm for solving least-squares problems and its convergence analysis
    Chen, Zhong
    Jianghan Shiyou Xueyuan Xuebao/Journal of Jianghan Petroleum Institute, 2002, 24 (01): : 92 - 93
  • [47] On the separable nonlinear least squares problems
    Liu, Xin
    Yuan, Yaxiang
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2008, 26 (03) : 390 - 403
  • [48] ON THE SEPARABLE NONLINEAR LEAST SQUARES PROBLEMS
    Xin Liu LSEC
    JournalofComputationalMathematics, 2008, 26 (03) : 390 - 403
  • [49] On the separable nonlinear least squares problems
    LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
    不详
    J Comput Math, 2008, 3 (390-403):
  • [50] A least squares method for solving biharmonic problems
    Thatcher, RW
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 38 (05) : 1523 - 1539
12345