Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative

Details Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative Continuous regularized Gauss-Newton-type algorithm for nonlinear ill-posed equations with simultaneous updates of inverse derivative

2001-03-28

arxiv.org/abs/math-ph/0103042v1

Physics

Mathematical Physics

10pp

Scientific paper

A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is proved. An attractive and novel feature of the proposed method is the absence of the assumptions about the location of the spectrum of the operator $F'(x)$. The absence of such assumptions is made possible by a source-type condition.

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