Continuous modified Newton’s-type method for nonlinear operator equations |
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Authors: | Alexander G. Ramm Alexandra B. Smirnova Angelo Favini |
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Affiliation: | (1) Mathematics Department, Kansas State University, Manhattan, KS 66506-2602, USA, e-mail: ramm@math.ksu.edu, US;(2) Department of Math and Stat, Georgia State University, Atlanta, GA 30303, USA, e-mail: smirn@cs.gsu.edu, US;(3) Dipartimento di Matematica, Universita di Bologna, 540127 Bologna, Italy, e-mail: favini@dm.unibo.it, IT |
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Abstract: | A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x 0 and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support |
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Keywords: | Mathematics Subject Classification (2000). 65J15, 58C15, 47H17 . nonlinear problem – integral inequality – Fréchet derivative – Newton method |
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