논문KCI 등재
The secant method and the generalized divided differences for solving nonlinear operator equations
0
조회
0
다운로드
0
인용
0
참고문헌
주제분류수학
초록
Abstract
We consider solving nonlinear operator equations using the secant method and the generalized divided dierences. We establish some local and semilocal convergence results for the proposed method. Numerical examplesand comparison with the work of others will be presented to demonstrate the efficiency of the method.
참고문헌 (20)
- Allgower, E.L., "Simplical and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations", SIAM Rev, 22, pp.28~85 (1980)
- Argyros, I. K, "On the Solution of Equations With Nondifferentiable Operators and the Ptak Error Estimates", BIT, 90, pp.752~754 (1990)
- Argyros, I. K, "On the Convergence of a Halley-Chebysheff Type Method Under Newton-Kantrovich Hypothesis", Appli. Math. Letters, 61, pp.71~74 (1993)
- Argyros, I. K, "On the Secant Method", Publ. Math. Debrecen, 43, pp.223~238 (1993)
- Attili, B. S, "An Iterative Method for Solving Nonlinear Operator Equations Using Generalized Divided Differences", Inter. J. Comput. Math, 79, pp.367~377 (2002)
- Brown, K. M, "A quadratically Convergent Newton Like Method Based Upon Gaussian Elimination", SIAMJ. Numer. Anal, 6(4), pp.560~569 (1969)
- Burden, R. L., "Numerical Analysis, 6th edition", pp.1997, Brooks
- Carnahan, B, "Applied Numerical Methods" (1969), Wiley, New York
- Chu, M. T, "Homotopy methods for general λ-matrix problem", SIAM J. Matrix Anal. Appl, 9, pp.528~536 (1988)
- Conte, S. D., "Elementary Numerical Analysis - An Algorithmic Approach, 3rd edition", pp.217~ (1980), McGraw-Hill
- Hernandez, M. A., "The Secant Method and Divided Differences Ho lder Continuous", Appl. Math. Comput, 124, pp.139~149 (2001)
- Ibidapo-Obe, O, "A newMethod for the Numerical Solution of Simultaneous Nonlinear Equations", Appl. Math. Comput, 125, pp.133~140 (2002)
- Kockler, N, "Numerical Methods and Scientific Computing" (1994), Clarendson Press, Oxford
- McCormick, S. F, "Multigrid Methods", pp.282~ (1987), SIAM Publications, Philadelphia, PA
- Paterson, W. R, "On Preferring Iterations in a Transformed Variable to the Method of Successive Substitution", Chem. Eng. Sci., 41, pp.601~602 (1986)
- Porta, F. A, "On an Iterative Algorithm of Order 1.839... for Solving Nonlinear Operator Equations", Numer. Funct. Anal. Optimiz., 7(1), pp.75~106 (1985)
- Scheurle, J.M, "Newton IterationsWithout Inverting the Derivative", Math. Meth. Appl. Sci., 1, pp.514~529 (1979)
- Seydel, R, "Practical Bifurcation and Stability Analysis - From Equilibrium to Chaos, 2nd edition", pp.166~ (1994), Springer-Verlag
- Verchelde, J, "Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems", SIAM J. Numer. Anal., 31, pp.915~930 (1994)
- Yamamoto, T, "On the Method of Tangent Hyperbolas in Banach Spaces", J. Comput. Appli. Math., 21, pp.75~86 (1988)
관련 논문AI추천
On a Quadratically Convergent Iterative Method Using Divided Differencesof Order OneIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2007 · 제14권 제3호LOCAL CONVERGENCE OF THE SECANT METHOD UPPER HOLDER CONTINUOUS DIVIDED DIFFERENCESIoannis K. Argyros영남수학회 · East Asian Mathematical Journal2008 · 제24권 제1호BROYDEN’S METHOD FOR OPERATORS WITH REGULARLY CONTINUOUS DIVIDED DIFFERENCESAnatoly M. Galperin대한수학회 · 대한수학회지2015 · 제52권 제1호Enlarging the ball of convergence of secant-like methods for non-differentiable operatorsHongmin Ren, IOANNISK.ARGYROS대한수학회 · 대한수학회지2018 · 제55권 제1호EXPANDING THE APPLICABILITY OF SECANT METHOD WITH APPLICATIONSA. Alberto Magre˜n´an, Ioannis K. Argyros대한수학회 · 대한수학회보2015 · 제52권 제3호A UNIFIED CONVERGENCE ANALYSIS FOR SECANT-TYPE METHODSAngel Alberto Magrenan, Ioannis Konstantinos Argyros대한수학회 · 대한수학회지2014 · 제51권 제6호
이 간행물의 다른 논문 (12건)
On a nonlinear system of functional difference equations with nonlinear complicated mixed maximaT. K. Yuldashevpp. 1-4Integer programming in an algebraic computation modelValentin E. Brimkov, Stefan S. Dantchevpp. 5-20On a class of conjectures equivalent to the strong Goldbach's conjecturePeter Vassilevpp. 21-26A linear operator and associated families of meromorphically multivalent functions of order aM. K. Aouf, H. M. Srivastavapp. 27-56A refinement of Carleman's inequalityJ. Cao, D.-W. Niu, F. Qipp. 57-62
