Some Geometric Constructions of Two Variants of Newton's Method to Solving Nonlinear Equations with Multiple Roots

被引：0
|
作者：
Cadenas, Carlos E. R. [1 ]
机构：
[1] Univ Carabobo, FaCyT, Dept Matemat, Valencia, Venezuela
来源：
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS | 2018年 / 50卷 / 01期
关键词：
Geometric construction; Newton's method; multiple roots; nonlinear equations;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give some geometric constructions of variations of Newton's method, based on ideas of Schroder, for the case that roots are multiple. A straight line and a polynomial are used to construct the iteration equation when the multiplicity of the root is known. In the case that the multiplicity is unknown another straight line and a rational function are used. Representative figures of an example are given.
引用
收藏
页码：15 / 21
页数：7
相关论文
共 50 条
  • [41] A QUASI-NEWTON METHOD FOR SOLVING NONLINEAR ALGEBRAIC EQUATIONS
    KIM, S
    TEWARSON, RP
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1992, 24 (04) : 93 - 97
  • [42] SSPH-Newton Iterative Method for Solving Nonlinear Equations
    Guan, Xuehao
    Wang, Rui
    INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2024, 21 (07)
  • [43] ON THE NEWTON-BROYDEN METHOD FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS
    Shakhno, S.
    Yarmola, H.
    JOURNAL OF APPLIED AND NUMERICAL ANALYSIS, 2023, 1 : 80 - 87
  • [44] A new family of Schroder's method and its variants based on power means for multiple roots of nonlinear equations
    Kanwar, V.
    Sharma, Kapil K.
    Behl, Ramandeep
    INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, 2010, 41 (04) : 558 - +
  • [45] Some new variants of Newton's method
    Özban, AY
    APPLIED MATHEMATICS LETTERS, 2004, 17 (06) : 677 - 682
  • [46] On the efficiency of two variants of Kurchatov's method for solving nonlinear systems
    Antonio Ezquerro, Jose
    Grau, Angela
    Grau-Sanchez, Miquel
    Angel Hernandez, Miguel
    NUMERICAL ALGORITHMS, 2013, 64 (04) : 685 - 698
  • [47] On the efficiency of two variants of Kurchatov’s method for solving nonlinear systems
    José Antonio Ezquerro
    Angela Grau
    Miquel Grau-Sánchez
    Miguel Ángel Hernández
    Numerical Algorithms, 2013, 64 : 685 - 698
  • [48] Modifying Kurchatov's method to find multiple roots of nonlinear equations
    Cordero, Alicia
    Garrido, Neus
    Torregrosa, Juan R.
    Triguero-Navarro, Paula
    APPLIED NUMERICAL MATHEMATICS, 2024, 198 : 11 - 21
  • [49] Some Novel Newton-Type Methods for Solving Nonlinear Equations
    Bisheh-Niasar, Morteza
    Saadatmandi, Abbas
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2020, 38 (03): : 111 - 123
  • [50] A Newton two-stage waveform relaxation method for solving systems of nonlinear algebraic equations
    Salkuyeh, Davod Khojasteh
    Hassanzadeh, Zeinab
    MATHEMATICAL COMMUNICATIONS, 2015, 20 (01) : 1 - 15
12345