×

A characterization of superlinear convergence and its application to quasi-Newton methods. (English) Zbl 0282.65042


MSC:

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] K. M. Brown & J. E. Dennis, Jr., ”A new algorithm for nonlinear least-squares curve fitting,” in Mathematical Software, John R. Rice, Editor, Academic Press, New York, 1971, pp. 391-396.
[2] C. G. Broyden, J. E. Dennis & J. J. Moré, On the Local and Superlinear Convergence of Quasi-Newton Methods, Cornell Computer Science Technical Report 72-137, 1972; J. Inst. Math. Appl. (To appear.)
[3] R. Fletcher, ”A new approach to variable metric algorithms,” Comput. J., v. 13, 1970, pp. 317-322. · Zbl 0207.17402
[4] A. A. Goldstein and J. F. Price, An effective algorithm for minimization, Numer. Math. 10 (1967), 184 – 189. · Zbl 0161.35402
[5] H. Y. Huang, Unified approach to quadratically convergent algorithms for function minimization, J. Optimization Theory Appl. 5 (1970), 405 – 423. · Zbl 0184.20202
[6] Garth P. McCormick and Klaus Ritter, Methods of conjugate directions versus quasi-Newton methods, Math. Programming 3 (1972), 101 – 116. · Zbl 0247.90055
[7] J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. · Zbl 0241.65046
[8] M. J. D. Powell, On the convergence of the variable metric algorithm, J. Inst. Math. Appl. 7 (1971), 21 – 36. · Zbl 0217.52804
[9] M. J. D. Powell, Private communication, 1972.
[10] K. Ritter, ”Superlinearly convergent methods for unconstrained minimization problems,” Proc. ACM, Boston, 1972, pp. 1137-1145.
[11] R. Voigt, Rates of Convergence for Iterative Methods for Nonlinear Systems of Equations, Ph.D. Thesis, University of Maryland, College Park, Md., 1969.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.