A characterization of superlinear convergence and its application to quasi-newton methods

Mathematics of Computation

Volumn 28, Issue 126, 1974, Pages 549-560

  Dennis, J E ^a   More, Jorge J ^a  

^a Department of Molecular Biology and Genetics   (United States)

Author keywords

Iterative methods for nonlinear equations; Quasi Newton methods; Superlinear convergence; Variable metric methods

Indexed keywords

EID: 84966259557     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1974-0343581-1     Document Type: Article

References (10)

1. K. M. Brown and J. E. Dennis, "A new algorithm for nonlinear least-squares curve fitting," in Mathematical Software, John R. Rice, Editor, Academic Press, New York, 1971, 391-396.
2. C. G. Broyden, J. E. Dennis and J. J. More, On the Local and Superlinear Convergence of Quasi Newton Methods, Cornell Computer Science Technical Report 72-137, 1972
3. R. Fletcher, "A new approach to variable metric algorithms," Comput. J., v. 13, 1970, 317-322.
4. A. Goldstein and J. Price, "An effective algorithm for minimization," Numer. Math., v. 10, 1967, 184-189
5. H. Y. Huang, "Unified approach to quadratically convergent algorithms for function minimization." 7. Optimization Theory Appl., v. 5, 1970, 405-423
6. G. McCormick and K. Ritter, "Methods of conjugate directions versus quasi-Newton methods," Math. Programming, v. 3, 1972, 101-116
7. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970
8. M. J. D. Powell, "On the convergence of the variable metric algorithm," 7. Inst. Math. Appl., v. 7, 1971, 21-36
9. K. Ritter, "Superlinearly convergent methods for unconstrained minimization problems," Proc. ACM, Boston, 1972, 1137-1145.
10. R. Voigt, Rates of Convergence for Iterative Methods for Nonlinear Systems of Equations, Ph.D. Thesis, University of Maryland, College Park, Md., 1969.