Modified minimal error method for nonlinear ill-posed problems.

*(English)*Zbl 1453.65123Summary: An error estimate for the minimal error method for nonlinear ill-posed problems under general a Hölder-type source condition is not known. We consider a modified minimal error method for nonlinear ill-posed problems. Using a Hölder-type source condition, we obtain an optimal order error estimate. We also consider the modified minimal error method with noisy data and provide an error estimate.

##### MSC:

65J15 | Numerical solutions to equations with nonlinear operators (do not use 65Hxx) |

65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |

##### Keywords:

nonlinear ill-posed problem; minimal error method; regularization method; discrepancy principle##### Software:

TIGRA
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\textit{M. Sabari} and \textit{S. George}, Comput. Methods Appl. Math. 18, No. 2, 313--321 (2018; Zbl 1453.65123)

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##### References:

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