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Contractors and secant methods for finding roots of non-linear functionals

Published online by Cambridge University Press:  09 April 2009

Mieczyslaw Altman
Mieczyslaw Altman
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales, 2308, Australia. Louisiana State University, Baton Rouge, Louisiana 70803, U. S. A.
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Abstract

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A further development of the concept of contractors for non-linear functionals is presented by introducing two-point contractors. On this basis two-point secant methods are proposed for finding roots of non-linear functionals in Banach spaces.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 1 , February 1975 , pp. 74 - 90
Copyright
Copyright © Australian Mathematical Society 1975

References

Altman, M. (1973), ‘Inverse differentiability, contractorsand equations in Banach spaces’, Studia Math., Vol. 46.Google Scholar
Altman, M. (1974), ‘Contractors with non-linear majorant functions and equations in Banach spaces’, Boll. U. M. I., 4 (9).Google Scholar
Altman, M., ‘Contractors and secant methods for solving equations’, (to appear).Google Scholar
Altman, M., ‘Contractors and roots of non-linear functionals’, (to appear (a)).Google Scholar
Ortega, J. M. and Rheinboldt, W. C. (1970), Iterative Solutions of Non-linear Equations in Several Variables, (Acad. Press, 1970.)Google Scholar