A Newton-Kantorovich-SOR type theorem

Béla Finta

Open Mathematics (2005)

  • Volume: 3, Issue: 2, page 282-293
  • ISSN: 2391-5455

Abstract

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In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.

How to cite

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Béla Finta. "A Newton-Kantorovich-SOR type theorem." Open Mathematics 3.2 (2005): 282-293. <http://eudml.org/doc/268904>.

@article{BélaFinta2005,
abstract = {In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.},
author = {Béla Finta},
journal = {Open Mathematics},
keywords = {46-00; 65-00},
language = {eng},
number = {2},
pages = {282-293},
title = {A Newton-Kantorovich-SOR type theorem},
url = {http://eudml.org/doc/268904},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Béla Finta
TI - A Newton-Kantorovich-SOR type theorem
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 282
EP - 293
AB - In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.
LA - eng
KW - 46-00; 65-00
UR - http://eudml.org/doc/268904
ER -

References

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  1. [1] N.S. Bahvalov: Numerical Methods, Technical Press, Budapest, 1977 (in Hungarian). 
  2. [2] R.G. Douglas: Banach Algebra Techniques in Operator Theory, Academic Press, New York and London, 1972. Zbl0247.47001
  3. [3] B. Finta: “Note about the iterative solutions of the nonlinear operator equations in finite dimensional spaces”, Research Seminars, Department of Mathematics, Technical University of Tg.Mures. Romania, Vol. 3, (1994), pp. 49–79. 
  4. [4] B. Finta: “Note about a method for solving nonlinear system of equations in finite dimensional spaces”, Studia Univ. Babes-Bolyai, Romania, Mathematica, XL, Vol. 1, (1995), pp. 59–64. 
  5. [5] B. Finta: “A Newton-Kantorovich-Seidel Type Theorem”, Publ. Univ. of Miskolc, Series D. natural Sciences, Hungary, Vol. 38, (1998), pp. 31–40. Zbl0924.65041
  6. [6] L.V. Kantorovich and G.P. Akilov: Functional Analysis in Normed Spaces, Academic Press, New York, 1978. 
  7. [7] J. Ortega and W. Rheinboldt: Local and global convergence of generalized linear iterations, Numerical solution of nonlinear problems, Soc. Ind. Appl. Math., Philadelphia, 1970. Zbl0224.65017
  8. [8] F. Szidarovszky and S. Yakowitz: Principles and Procedures of Numerical Analysis, Plenum Press, New York and London, 1978. 
  9. [9] V.A. Wertheim: “On the conditions for the application of Newton's method”, D.A.N., Vol. 110, (1956), pp. 719–722. Zbl0072.13601

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