메뉴 건너뛰기




Volumn 32, Issue 2, 2003, Pages 249-260

Globally convergent inexact quasi-Newton methods for solving nonlinear systems

Author keywords

Global convergence; Inexact Newton methods; Nonlinear systems; Quasi Newton methods; Superlinear convergence

Indexed keywords


EID: 0037528024     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1024013824524     Document Type: Article
Times cited : (60)

References (24)
  • 1
    • 0009961734 scopus 로고
    • A new sparsity-preserving quasi-Newton update for solving nonlinear equations
    • I.D.L. Bogle and J.D. Perkins, A new sparsity-preserving quasi-Newton update for solving nonlinear equations, SIAM J. Scientific Statist. Comput. 11 (1990) 621-630.
    • (1990) SIAM J. Scientific Statist. Comput. , vol.11 , pp. 621-630
    • Bogle, I.D.L.1    Perkins, J.D.2
  • 2
    • 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
  • 3
    • 84984075899 scopus 로고
    • On superlinear convergence of some stable variants of the secant method
    • O. Burdakov, On superlinear convergence of some stable variants of the secant method, ZAMM 66 (1986) 615-622.
    • (1986) ZAMM , vol.66 , pp. 615-622
    • Burdakov, O.1
  • 5
    • 0002663672 scopus 로고
    • A characterization of superlinear convergence and its applications to quasi-Newton methods
    • J.E. Dennis Jr. and J.J. Moré, A characterization of superlinear convergence and its applications to quasi-Newton methods, SIAM Rev. 19 (1977) 46-89.
    • (1977) SIAM Rev. , vol.19 , pp. 46-89
    • Dennis Jr., J.E.1    Moré, J.J.2
  • 7
    • 0000947761 scopus 로고
    • Convergence theorems for least-change secant update methods
    • J.E. Dennis Jr. and H.F. Walker, Convergence theorems for least-change secant update methods, SIAM J. Numer. Anal. 18 (1981) 949-987.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 949-987
    • Dennis Jr., J.E.1    Walker, H.F.2
  • 8
    • 0001330894 scopus 로고
    • Globally convergent inexact Newton methods
    • S.C. Eisenstat and H.F. Walker, Globally convergent inexact Newton methods, SIAM J. Optim. 4 (1994) 392-422.
    • (1994) SIAM J. Optim. , vol.4 , pp. 392-422
    • Eisenstat, S.C.1    Walker, H.F.2
  • 9
    • 0346721147 scopus 로고
    • Solving systems of nonlinear equations by Broyden's method with projected updates
    • eds. O. Mangasarian, R. Meyer and S. Robinson (Academic Press, New York
    • D.M. Gay and R.B. Schnabel, Solving systems of nonlinear equations by Broyden's method with projected updates, in: Nonlinear Programming, Vol. 3, eds. O. Mangasarian, R. Meyer and S. Robinson (Academic Press, New York, 1978) pp. 245-281.
    • (1978) Nonlinear Programming , vol.3 , pp. 245-281
    • Gay, D.M.1    Schnabel, R.B.2
  • 10
    • 0348004939 scopus 로고
    • The column-updating method for solving nonlinear equations in Hubert space
    • M.A. Gomes-Ruggiero and J.M. Martínez, The column-updating method for solving nonlinear equations in Hubert space, RAIRO Math. Modelling Numer. Anal. 26 (1992) 309-330.
    • (1992) RAIRO Math. Modelling Numer. Anal. , vol.26 , pp. 309-330
    • Gomes-Ruggiero, M.A.1    Martínez, J.M.2
  • 12
    • 0343100570 scopus 로고    scopus 로고
    • A globally convergent inexact-Newton method for solving reducible nonlinear systems of equations
    • N. Krejić and J.M. Martínez, A globally convergent inexact-Newton method for solving reducible nonlinear systems of equations, Optim. Methods Software 13 (2000) 11-34.
    • (2000) Optim. Methods Software , vol.13 , pp. 11-34
    • Krejić, N.1    Martínez, J.M.2
  • 13
    • 0033645092 scopus 로고    scopus 로고
    • Derivative-free line search and global convergence of Broyden-like method for nonlinear equations
    • D.-H. Li and M. Fukushima, Derivative-free line search and global convergence of Broyden-like method for nonlinear equations, Optim. Methods Software 13 (2000) 181-201.
    • (2000) Optim. Methods Software , vol.13 , pp. 181-201
    • Li, D.-H.1    Fukushima, M.2
  • 14
    • 84973022113 scopus 로고
    • Convergence properties of the inverse column-updating method
    • V.L.R. Lopes and J.M. Martínez, Convergence properties of the inverse column-updating method, Optim. Methods Software 6 (1995) 127-144.
    • (1995) Optim. Methods Software , vol.6 , pp. 127-144
    • Lopes, V.L.R.1    Martínez, J.M.2
  • 15
    • 0031651231 scopus 로고    scopus 로고
    • Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations
    • L. Lukšan and J. Vlček, Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations, Optim. Methods Software 8 (1998) 185-199.
    • (1998) Optim. Methods Software , vol.8 , pp. 185-199
    • Lukšan, L.1    Vlček, J.2
  • 16
    • 0018689918 scopus 로고
    • Three new algorithms based on the sequential secant method
    • J.M. Martínez, Three new algorithms based on the sequential secant method, BIT 19 (1979) 236-243.
    • (1979) BIT , vol.19 , pp. 236-243
    • Martínez, J.M.1
  • 17
    • 0021614679 scopus 로고
    • A quasi-Newton method with modification of one column per iteration
    • J.M. Martínez, A quasi-Newton method with modification of one column per iteration, Computing 33 (1984) 353-362.
    • (1984) Computing , vol.33 , pp. 353-362
    • Martínez, J.M.1
  • 18
    • 0038411679 scopus 로고
    • Algorithms for solving nonlinear systems of equations, in: Continuous Optimization
    • ed. E. Spedicato (Kluwer Academic, Dordrecht)
    • J.M. Martínez, Algorithms for solving nonlinear systems of equations, in: Continuous Optimization. The State of Art, ed. E. Spedicato (Kluwer Academic, Dordrecht, 1994) pp. 81-108.
    • (1994) The State of Art , pp. 81-108
    • Martínez, J.M.1
  • 19
    • 84966215619 scopus 로고
    • Local convergence theory of inexact Newton methods based on structured least change updates
    • J.M. Martínez, Local convergence theory of inexact Newton methods based on structured least change updates, Math. Comp. 55 (1990) 143-167.
    • (1990) Math. Comp. , vol.55 , pp. 143-167
    • Martínez, J.M.1
  • 20
    • 0034545378 scopus 로고    scopus 로고
    • Practical quasi-Newton methods for solving nonlinear systems
    • J.M. Martínez, Practical quasi-Newton methods for solving nonlinear systems, J. Comput. Appl. Math. 124 (2000) 97-122.
    • (2000) J. Comput. Appl. Math. , vol.124 , pp. 97-122
    • Martínez, J.M.1
  • 21
    • 84972904922 scopus 로고
    • An inverse column-updating method for solving large scale non-linear systems of equations
    • J.M. Martínez and M.C. Zambaldi, An inverse column-updating method for solving large scale non-linear systems of equations, Optim. Methods Software 1 (1992) 129-140.
    • (1992) Optim. Methods Software , vol.1 , pp. 129-140
    • Martínez, J.M.1    Zambaldi, M.C.2
  • 22
    • 0346113612 scopus 로고
    • On the convergence of inexact quasi-Newton methods
    • I. Moret, On the convergence of inexact quasi-Newton methods, Internat. J. Comput. Math. 28 (1989) 117-137.
    • (1989) Internat. J. Comput. Math. , vol.28 , pp. 117-137
    • Moret, I.1
  • 23
    • 84966239443 scopus 로고
    • Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian
    • L.K. Schubert, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Math. Comp. 24 (1970) 27-30.
    • (1970) Math. Comp. , vol.24 , pp. 27-30
    • Schubert, L.K.1
  • 24
    • 34250502027 scopus 로고
    • A modification of Newton's method
    • V.E. Shamanski, A modification of Newton's method, Ukrain Mat. Z. 19 (1967) 133-138.
    • (1967) Ukrain Mat. Z. , vol.19 , pp. 133-138
    • Shamanski, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.