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.
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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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Ramm, A., Smirnova, A. & Favini, A. Continuous modified Newton’s-type method for nonlinear operator equations. Ann. Mat. Pura Appl. IV. Ser. 182, 37–52 (2003). https://doi.org/10.1007/s10231-002-0054-0
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DOI: https://doi.org/10.1007/s10231-002-0054-0