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Volumn 33, Issue 1-4, 2003, Pages 123-135

A classification of quasi-Newton methods

Author keywords

Nonlinear equations; Quasi Newton methods

Indexed keywords


EID: 0042878519     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025551602679     Document Type: Conference Paper
Times cited : (34)

References (35)
  • 1
    • 0347374776 scopus 로고
    • On the approximate solutions of operator equations in Hilbert space
    • M. Altman, On the approximate solutions of operator equations in Hilbert space, Bull. Pol. Acad. Sci. Math. 5 (1957) 605-609.
    • (1957) Bull. Pol. Acad. Sci. Math. , vol.5 , pp. 605-609
    • Altman, M.1
  • 2
    • 84945709150 scopus 로고
    • Iterative procedures for nonlinear integral equations
    • D. Anderson, Iterative procedures for nonlinear integral equations, J. Assoc. Comput. Mach. 12 (1965) 547-560.
    • (1965) J. Assoc. Comput. Mach. , vol.12 , pp. 547-560
    • Anderson, D.1
  • 3
    • 0041708327 scopus 로고
    • An algorithm for solving nonlinear equations based on the secant method
    • J.G.P. Barnes, An algorithm for solving nonlinear equations based on the secant method, Computer J. 8 (1965) 66-72.
    • (1965) Computer J. , vol.8 , pp. 66-72
    • Barnes, J.G.P.1
  • 4
    • 0001531895 scopus 로고
    • Two-point step size gradient methods
    • J. Barzilai and J.M. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal. 8 (1988) 141-148.
    • (1988) IMA J. Numer. Anal. , vol.8 , pp. 141-148
    • Barzilai, J.1    Borwein, J.M.2
  • 5
    • 0005323285 scopus 로고
    • Application de l'ε-algorithme à la résolution des systèmes non linéaires
    • C. Brezinski, Application de l'ε-algorithme à la résolution des systèmes non linéaires, C. R. Acad. Sci. Paris A 271 (1970) 1174-1177.
    • (1970) C. R. Acad. Sci. Paris A , vol.271 , pp. 1174-1177
    • Brezinski, C.1
  • 6
    • 0016452789 scopus 로고
    • Numerical stability of a quadratic method for solving systems of nonlinear equations
    • C. Brezinski, Numerical stability of a quadratic method for solving systems of nonlinear equations, Computing 14 (1975) 205-211.
    • (1975) Computing , vol.14 , pp. 205-211
    • Brezinski, C.1
  • 7
    • 0020932720 scopus 로고
    • Recursive interpolation, extrapolation and projection
    • C. Brezinski, Recursive interpolation, extrapolation and projection, J. Comput. Appl. Math. 9 (1983) 369-376.
    • (1983) J. Comput. Appl. Math. , vol.9 , pp. 369-376
    • Brezinski, C.1
  • 9
    • 0032487164 scopus 로고    scopus 로고
    • Vector sequence transformations: Methodology and applications to linear systems
    • C. Brezinski, Vector sequence transformations: Methodology and applications to linear systems, J. Comput. Appl. Math. 98 (1998) 149-175.
    • (1998) J. Comput. Appl. Math. , vol.98 , pp. 149-175
    • Brezinski, C.1
  • 10
    • 0039255508 scopus 로고    scopus 로고
    • Dynamical systems and sequence transformations
    • C. Brezinski, Dynamical systems and sequence transformations, J. Phys. A: Math. Gen. 34 (2001) 10659-10669.
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 10659-10669
    • Brezinski, C.1
  • 11
    • 0036643369 scopus 로고    scopus 로고
    • Biorthogonal vector sequence transformations and Padé approximation of vector series
    • C. Brezinski, Biorthogonal vector sequence transformations and Padé approximation of vector series, Appl. Numer. Math. 41 (2002) 437-442.
    • (2002) Appl. Numer. Math. , vol.41 , pp. 437-442
    • Brezinski, C.1
  • 12
    • 0032117188 scopus 로고    scopus 로고
    • Nonlinear hybrid procedures and fixed point iterations
    • C. Brezinski and J.-P. Chehab, Nonlinear hybrid procedures and fixed point iterations, Numer. Funct. Anal. Optimization 19 (1998) 465-487.
    • (1998) Numer. Funct. Anal. Optimization , vol.19 , pp. 465-487
    • Brezinski, C.1    Chehab, J.-P.2
  • 13
    • 0033293666 scopus 로고    scopus 로고
    • Multiparameter iterative schemes for the solution of systems of linear and nonlinear equations
    • C. Brezinski and J.-P. Chehab, Multiparameter iterative schemes for the solution of systems of linear and nonlinear equations, SIAM J. Sci. Comput. 20 (1999) 2140-2159.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 2140-2159
    • Brezinski, C.1    Chehab, J.-P.2
  • 15
    • 0038981549 scopus 로고
    • Vector sequence transformations and fixed point methods
    • eds. C. Taylor et al. (Pineridge Press, Swansea)
    • C. Brezinski and H. Sadok, Vector sequence transformations and fixed point methods, in: Numerical Methods in Laminar and Turbulent Flows, Vol. I, eds. C. Taylor et al. (Pineridge Press, Swansea, 1987) pp. 3-11.
    • (1987) Numerical Methods in Laminar and Turbulent Flows , vol.1 , pp. 3-11
    • Brezinski, C.1    Sadok, H.2
  • 16
    • 84968510937 scopus 로고
    • A class of methods for solving nonlinear simultaneous equations
    • C.G. Broyden, A class of methods for solving nonlinear simultaneous equations, Math. Comp. 19 (1965) 577-593.
    • (1965) Math. Comp. , vol.19 , pp. 577-593
    • Broyden, C.G.1
  • 17
    • 0010276776 scopus 로고
    • A nonlinear adaptative multiresolution method in finite differences with incremental unknowns
    • J.-P. Chehab, A nonlinear adaptative multiresolution method in finite differences with incremental unknowns, Modél. Math. Anal. Numér. 29 (1995) 451-475.
    • (1995) Modél. Math. Anal. Numér. , vol.29 , pp. 451-475
    • Chehab, J.-P.1
  • 18
    • 0003264499 scopus 로고
    • Variable metric methods for minimization
    • Argonne National Laboratory, Argonne, IL, USA
    • W. Davidon, Variable metric methods for minimization, A.E.C. Res. and Develop. Report ANL-5990, Argonne National Laboratory, Argonne, IL, USA (1959).
    • (1959) A.E.C. Res. and Develop. Report , vol.ANL-5990
    • Davidon, W.1
  • 19
    • 84966259557 scopus 로고
    • A characterization of superlinear convergence and its applications to quasi-Newton methods
    • I.E. Dennis and J.J. Moré, A characterization of superlinear convergence and its applications to quasi-Newton methods, Math. Comp. 28 (1974) 549-560.
    • (1974) Math. Comp. , vol.28 , pp. 549-560
    • Dennis, I.E.1    Moré, J.J.2
  • 21
    • 0000387235 scopus 로고
    • A rapidly convergent descent method for minimization
    • R. Fletcher and M. Powell, A rapidly convergent descent method for minimization, Comput. J. 6 (1963) 163-168.
    • (1963) Comput. J. , vol.6 , pp. 163-168
    • Fletcher, R.1    Powell, M.2
  • 22
    • 84966252930 scopus 로고
    • On the solution of systems of equations by the epsilon algorithm of Wynn
    • E. Gekeler, On the solution of systems of equations by the epsilon algorithm of Wynn, Math. Comp. 26 (1972) 427-436.
    • (1972) Math. Comp. , vol.26 , pp. 427-436
    • Gekeler, E.1
  • 24
    • 0001003956 scopus 로고
    • Some results about vector extrapolation methods and related fixed-point iterations
    • K. Jbilou and H. Sadok, Some results about vector extrapolation methods and related fixed-point iterations, J. Comput. Appl. Math. 36 (1991) 385-398.
    • (1991) J. Comput. Appl. Math. , vol.36 , pp. 385-398
    • Jbilou, K.1    Sadok, H.2
  • 26
    • 0000168478 scopus 로고
    • The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations
    • H. Le Ferrand, The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations, Numer. Algorithms 3 (1992) 273-284.
    • (1992) Numer. Algorithms , vol.3 , pp. 273-284
    • Le Ferrand, H.1
  • 27
    • 0346744400 scopus 로고
    • Une méthode de résolution de certains systèmes non linéaires bien posés
    • C. Lemaréchal, Une méthode de résolution de certains systèmes non linéaires bien posés, C. R. Acad. Sci. Paris Sér. A 272 (1971) 605-607.
    • (1971) C. R. Acad. Sci. Paris Sér. A , vol.272 , pp. 605-607
    • Lemaréchal, C.1
  • 28
    • 0014793954 scopus 로고
    • A bifurcation problem in E-layer equilibria
    • B. Marder and H. Weitzner, A bifurcation problem in E-layer equilibria, Plasma Phys. 12 (1970) 435-445.
    • (1970) Plasma Phys. , vol.12 , pp. 435-445
    • Marder, B.1    Weitzner, H.2
  • 30
    • 0011739235 scopus 로고
    • On the Barzilai and Borwein choice of steplength for the gradient method
    • M. Raydan, On the Barzilai and Borwein choice of steplength for the gradient method, IMA J. Numer. Anal. 13 (1993) 321-326.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 321-326
    • Raydan, M.1
  • 32
    • 0025254797 scopus 로고
    • About Henrici's transformation for accelerating vector sequences
    • H. Sadok, About Henrici's transformation for accelerating vector sequences, J. Comput. Appl. Math. 29 (1990) 101-110.
    • (1990) J. Comput. Appl. Math. , vol.29 , pp. 101-110
    • Sadok, H.1
  • 34
    • 0347374772 scopus 로고
    • On a discrete version of the Newton-Raphson method
    • L. Wegge, On a discrete version of the Newton-Raphson method, SIAM J. Numer. Anal. 3 (1966) 134-142.
    • (1966) SIAM J. Numer. Anal. , vol.3 , pp. 134-142
    • Wegge, L.1
  • 35
    • 84945709863 scopus 로고
    • The secant method for simultaneous nonlinear equations
    • P. Wolfe, The secant method for simultaneous nonlinear equations, Commun. ACM 2 (1959) 12-13.
    • (1959) Commun. ACM , vol.2 , pp. 12-13
    • Wolfe, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.