Abstract
A solution of a nonlinear equation in Hilbert spaces is said to be a simple singular solution if the Frechet derivative at the solution has one-dimensional kernel and cokernel. In this paper we present the enlargement procedure for resolution of singularities at simple singular solutions of nonlinear equations. Once singularities are resolved, we can compute accurately the singular solution by Newton's method. Conditions for which the procedure terminates in finite steps are given. In particular, if the equation defined in ?n is analytic and the simple singular solution is geometrically isolated, the procedure stops in finite steps, and we obtain the enlarged problem with an isolated solution. Numerical examples are given.
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