메뉴 건너뛰기




Volumn 10, Issue 1, 1998, Pages 79-103

Quadratic and superlinear convergence of the huschens method for nonlinear least squares problems

Author keywords

Broyden family; Huschens method; Nonlinear least squares problem; Quadratic and superlinear convergence; Structured quasi Newton method

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; ITERATIVE METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING; LEAST SQUARES APPROXIMATIONS;

EID: 0032047409     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018391917880     Document Type: Article
Times cited : (9)

References (17)
  • 2
    • 0001159416 scopus 로고
    • The estimation of the Hessian matrix in nonlinear least squares problems with non-zero residuals
    • M. C. Bartholomew-Biggs, "The estimation of the Hessian matrix in nonlinear least squares problems with non-zero residuals," Mathematical Programming, vol. 12, pp. 67-80, 1977.
    • (1977) Mathematical Programming , vol.12 , pp. 67-80
    • Bartholomew-Biggs, M.C.1
  • 4
    • 0001184183 scopus 로고
    • Convergence theory for the structured BFGS secant method with an application to nonlinear least squares
    • J. E. Dennis, Jr., H. J. Martinez, and R. A. Tapia, "Convergence theory for the structured BFGS secant method with an application to nonlinear least squares," Journal of Optimization Theory and Applications, vol. 61, pp. 161-178, 1989.
    • (1989) Journal of Optimization Theory and Applications , vol.61 , pp. 161-178
    • Dennis Jr., J.E.1    Martinez, H.J.2    Tapia, R.A.3
  • 5
    • 84966259557 scopus 로고
    • A characterization of superlinear convergence and its application to quasi-Newton methods
    • J. E. Dennis, Jr. and J. J. More, "A characterization of superlinear convergence and its application to quasi-Newton methods," Mathematics of Computation, vol. 28, pp. 549-560, 1974.
    • (1974) Mathematics of Computation , vol.28 , pp. 549-560
    • Dennis Jr., J.E.1    More, 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 Journal on Numerical Analysis, vol. 18, pp. 949-987, 1981.
    • (1981) SIAM Journal on Numerical Analysis , vol.18 , pp. 949-987
    • Dennis Jr., J.E.1    Walker, H.F.2
  • 8
    • 84964329988 scopus 로고
    • Local and superlinear convergence for partially known quasi-Newton methods
    • J. R. Engels and H. J. Martinez, "Local and superlinear convergence for partially known quasi-Newton methods," SIAM Journal on Optimization, vol. 1, pp. 42-56, 1991.
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 42-56
    • Engels, J.R.1    Martinez, H.J.2
  • 9
    • 0000308182 scopus 로고
    • Hybrid methods for nonlinear least squares
    • R. Fletcher and C. Xu, "Hybrid methods for nonlinear least squares," IMA Journal of Numerical Analysis, vol. 7, pp. 371-389, 1987.
    • (1987) IMA Journal of Numerical Analysis , vol.7 , pp. 371-389
    • Fletcher, R.1    Xu, C.2
  • 10
    • 10044258399 scopus 로고
    • Structured quasi-Newton methods for optimization problems in Hubert spaces
    • Universität Trier, Trier, Germany, June
    • J. Huschens, "Structured quasi-Newton methods for optimization problems in Hubert spaces," Technical report, Universität Trier, Trier, Germany, June 1991.
    • (1991) Technical Report
    • Huschens, J.1
  • 11
    • 0002178198 scopus 로고
    • On the use of product structure in secant methods for nonlinear least squares problems
    • J. Huschens, " On the use of product structure in secant methods for nonlinear least squares problems," SIAM Journal on Optimization, vol. 4, pp. 108-129, 1994.
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 108-129
    • Huschens, J.1
  • 13
    • 0009223768 scopus 로고
    • Superlinear convergence of Broyden's bounded θ-class of methods
    • A. Stachurski, "Superlinear convergence of Broyden's bounded θ-class of methods," Mathematical Programming, vol. 20, pp. 196-212, 1981.
    • (1981) Mathematical Programming , vol.20 , pp. 196-212
    • Stachurski, A.1
  • 14
    • 2442573166 scopus 로고
    • On Huschens method for solving nonlinear least squares problems
    • Science University of Tokyo in Japanese
    • H. Yabe, "On Huschens method for solving nonlinear least squares problems," in Studies in Liberal Arts and Sciences, vol. 26, pp. 217-231. Science University of Tokyo, 1993, in Japanese.
    • (1993) Studies in Liberal Arts and Sciences , vol.26 , pp. 217-231
    • Yabe, H.1
  • 15
    • 0026191354 scopus 로고
    • Factorized quasi-Newton methods for nonlinear least squares problems
    • H. Yabe and T. Takahashi, "Factorized quasi-Newton methods for nonlinear least squares problems," Mathematical Programming, vol. 51, pp. 75-100, 1991.
    • (1991) Mathematical Programming , vol.51 , pp. 75-100
    • Yabe, H.1    Takahashi, T.2
  • 16
    • 21844505007 scopus 로고
    • Convergence of a faetorized Broyden-like family for nonlinear least squares problems
    • H. Yabe and N. Yamaki, "Convergence of a faetorized Broyden-like family for nonlinear least squares problems," SIAM Journal on Optimization, vol. 5, pp. 770-791, 1995.
    • (1995) SIAM Journal on Optimization , vol.5 , pp. 770-791
    • Yabe, H.1    Yamaki, N.2
  • 17
    • 0042067937 scopus 로고    scopus 로고
    • Local and superlinear convergence of structured quasi-Newton methods for nonlinear optimization
    • H. Yabe and N. Yamaki, "Local and superlinear convergence of structured quasi-Newton methods for nonlinear optimization," Journal of the Operations Research Society of Japan, vol. 39, pp. 541-557, 1996.
    • (1996) Journal of the Operations Research Society of Japan , vol.39 , pp. 541-557
    • Yabe, H.1    Yamaki, N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.