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- W4291237785 abstract "Lavrent'ev regularization for the autoconvolution equation was considered by J. Janno in {itshape Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution equation}, Inverse Problems, 16(2):333--348, 2000. Here this study is extended by considering discretization of the Lavrent'ev scheme by splines. It is shown how to maintain the known convergence rate by an appropriate choice of spline spaces and a proper choice of the discretization level. For piece-wise constant splines the discretized equation allows for an explicit solver, in contrast to using higher order splines. This is used to design a fast implementation by means of post-smoothing, which provides results, which are indistinguishable from results obtained by direct discretization using cubic splines." @default.
- W4291237785 created "2022-08-13" @default.
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- W4291237785 date "2016-04-12" @default.
- W4291237785 modified "2023-09-24" @default.
- W4291237785 title "Discretized Lavrent' ev regularization for the autoconvolution equation" @default.
- W4291237785 doi "https://doi.org/10.48550/arxiv.1604.03275" @default.
- W4291237785 hasPublicationYear "2016" @default.
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