Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T23:00:35.072Z Has data issue: false hasContentIssue false
  • English
  • Français

On the monotone convergence of general Newton-like methods

Published online by Cambridge University Press:  17 April 2009

Ioannis K. Argyros  and
Ferenc Szidarovszky
Ioannis K. Argyros
Affiliation:
Cameron UniversityDepartment of Mathematics Lawton, OK 73505-6377United States of America
Ferenc Szidarovszky
Affiliation:
Department of Systems andIndustrial Engineering University of ArizonaTucson AZ 85721United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper examines conditions for the monotone convergence of general Newton-like methods generated by point-to-point mappings. The speed of convergence of such mappings is also examined.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 3 , June 1992 , pp. 489 - 502
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Argyros, I.K., ‘On the secant method and fixed points of nonlinear equations’, Monatsh. Math. 106 (1988), 85–94.Google Scholar
[2]Baluev, A., ‘On the method of Chaplygin’, Dokl. Akad. Nauk. SSSR 83 (1952), 781–784. (In Russian)Google Scholar
[3]Dennis, J.E., ‘Toward a unified convergence theory for Newton-like methods’, in Nonlinear functional analysis and applications, Editor Rall, L.B., pp. 425–472 (Academic Press, New York, 1971).CrossRefGoogle Scholar
[4]Fujimoto, T., ‘Global asymptotic stability of nonlinear difference equations’, I. Econ. Letters 22 (1987), 247–250.Google Scholar
[5]Kantorovich, L.V. and Akilov, G.P., Functional analysis in normed spaces (Pergamon Press, New York, 1964).Google Scholar
[6]Krasnoleskii, M.A., Positive solutions of operator equations (Noordhoff, Groningen, 1964).Google Scholar
[7]La Salle, J.P., The stability and control of discrete processes (Springer-Verlag, New York, 1968).Google Scholar
[8]Okuguchi, K., Mathematical foundation of economic analysis (McGraw-Hill, Tokyo, 1977). (In Japanese).Google Scholar
[9]Okuguchi, K. and Szidarovszky, F., Theory of oligopoly with multi-product firms (Springer-Verlag, New York, 1990).CrossRefGoogle Scholar
[10]Potra, F.A., ‘Monotone iterative methods for nonlinear operator equations’, Numer. Funct. Anal. Optim. 9 (7, 8) (1987), 809–843.CrossRefGoogle Scholar
[11]Slugin, S., ‘On the theory of Newton's and Chaplygin's method’, (In Russian), Dokl. Akad. Nauk. SSSR 120 (1958), 472–474.Google Scholar
[12]Tishyadhigama, S., Polak, E. and Klessig, R., ‘A comparative study of several convergence conditions for algorithms modeled by point-to-set maps’, Math. Programming Stud. 10 (1979), 172–190.CrossRefGoogle Scholar
[13]Tarskii, A.A., ‘A lattice theoretical fixed point theorem and its applications’, Pacific J. Math. (1955), 285–309.CrossRefGoogle Scholar