A Newton-Kantorovich-SOR type theorem

• Autorzy: Béla Finta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Iterative method; Newton method; SOR method; 46-00; 65-00

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 282-293

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

Béla Finta

• Petru Maior University of Tg. Mures

Bibliografia

• [1] N.S. Bahvalov: Numerical Methods, Technical Press, Budapest, 1977 (in Hungarian).
• [2] R.G. Douglas: Banach Algebra Techniques in Operator Theory, Academic Press, New York and London, 1972.
• [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] 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] B. Finta: “A Newton-Kantorovich-Seidel Type Theorem”, Publ. Univ. of Miskolc, Series D. natural Sciences, Hungary, Vol. 38, (1998), pp. 31–40.
• [6] L.V. Kantorovich and G.P. Akilov: Functional Analysis in Normed Spaces, Academic Press, New York, 1978.
• [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.
• [8] F. Szidarovszky and S. Yakowitz: Principles and Procedures of Numerical Analysis, Plenum Press, New York and London, 1978.
• [9] V.A. Wertheim: “On the conditions for the application of Newton's method”, D.A.N., Vol. 110, (1956), pp. 719–722.

Identyfikatory

DOI

10.2478/BF02479204