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      The secant method and the generalized divided differences for solving nonlinear operator equations

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      https://www.riss.kr/link?id=A104869196

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      다국어 초록 (Multilingual 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...

      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.

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      참고문헌 (Reference)

      1 Hernandez, M. A., "The Secant Method and Divided Differences Ho lder Continuous" 124 : 139-149, 2001

      2 Allgower, E.L., "Simplical and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations" 22 : 28-85, 1980

      3 Seydel, R, "Practical Bifurcation and Stability Analysis - From Equilibrium to Chaos, 2nd edition" Springer-Verlag 166-, 1994

      4 Argyros, I. K, "On the Solution of Equations With Nondifferentiable Operators and the Ptak Error Estimates" 90 : 752-754, 1990

      5 Argyros, I. K, "On the Secant Method" 43 : 223-238, 1993

      6 Yamamoto, T, "On the Method of Tangent Hyperbolas in Banach Spaces" 21 : 75-86, 1988

      7 Argyros, I. K, "On the Convergence of a Halley-Chebysheff Type Method Under Newton-Kantrovich Hypothesis" 61 : 71-74, 1993

      8 Porta, F. A, "On an Iterative Algorithm of Order 1.839... for Solving Nonlinear Operator Equations" 7 (7): 75-106, 1985

      9 Paterson, W. R, "On Preferring Iterations in a Transformed Variable to the Method of Successive Substitution" 41 : 601-602, 1986

      10 Kockler, N, "Numerical Methods and Scientific Computing" Clarendson Press, Oxford 1994

      1 Hernandez, M. A., "The Secant Method and Divided Differences Ho lder Continuous" 124 : 139-149, 2001

      2 Allgower, E.L., "Simplical and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations" 22 : 28-85, 1980

      3 Seydel, R, "Practical Bifurcation and Stability Analysis - From Equilibrium to Chaos, 2nd edition" Springer-Verlag 166-, 1994

      4 Argyros, I. K, "On the Solution of Equations With Nondifferentiable Operators and the Ptak Error Estimates" 90 : 752-754, 1990

      5 Argyros, I. K, "On the Secant Method" 43 : 223-238, 1993

      6 Yamamoto, T, "On the Method of Tangent Hyperbolas in Banach Spaces" 21 : 75-86, 1988

      7 Argyros, I. K, "On the Convergence of a Halley-Chebysheff Type Method Under Newton-Kantrovich Hypothesis" 61 : 71-74, 1993

      8 Porta, F. A, "On an Iterative Algorithm of Order 1.839... for Solving Nonlinear Operator Equations" 7 (7): 75-106, 1985

      9 Paterson, W. R, "On Preferring Iterations in a Transformed Variable to the Method of Successive Substitution" 41 : 601-602, 1986

      10 Kockler, N, "Numerical Methods and Scientific Computing" Clarendson Press, Oxford 1994

      11 Burden, R. L., "Numerical Analysis, 6th edition" Brooks/Cole 611-, 1997

      12 Scheurle, J.M, "Newton IterationsWithout Inverting the Derivative" 1 : 514-529, 1979

      13 McCormick, S. F, "Multigrid Methods" SIAM Publications, Philadelphia, PA 282-, 1987

      14 Chu, M. T, "Homotopy methods for general λ-matrix problem" 9 : 528-536, 1988

      15 Verchelde, J, "Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems" 31 : 915-930, 1994

      16 Conte, S. D., "Elementary Numerical Analysis - An Algorithmic Approach, 3rd edition" McGraw-Hill 217-, 1980

      17 Carnahan, B, "Applied Numerical Methods" Wiley, New York 1969

      18 Attili, B. S, "An Iterative Method for Solving Nonlinear Operator Equations Using Generalized Divided Differences" 79 : 367-377, 2002

      19 Brown, K. M, "A quadratically Convergent Newton Like Method Based Upon Gaussian Elimination" 6 (6): 560-569, 1969

      20 Ibidapo-Obe, O, "A newMethod for the Numerical Solution of Simultaneous Nonlinear Equations" 125 : 133-140, 2002

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      2024 평가예정 해외DB학술지평가 신청대상 (해외등재 학술지 평가)
      2021-01-01 평가 등재학술지 선정 (해외등재 학술지 평가) KCI등재
      2020-12-01 평가 등재 탈락 (해외등재 학술지 평가)
      2013-10-01 평가 등재학술지 선정 (기타) KCI등재
      2011-01-01 평가 등재후보학술지 유지 (기타) KCI등재후보
      2008-04-08 학회명변경 한글명 : 장전수리과학회 -> 장전수학회(章田數學會) KCI등재후보
      2008-01-01 평가 SCOPUS 등재 (신규평가) KCI등재후보
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