Continuous modified Newton's-type method for nonlinear operator equations
A. G. Ramm, A. B. Smirnova, A. Favini
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 x0 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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