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The L-pseudo-solution using stochastic algorithm of Landweber

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Abstract

In this paper, we consider a linear equation Ax=u. A is an operator with an unbounded inverse in a Hilbert space. The right side u does not belong to the range of A. Obviously, a solution in classical sense does not exist and A −1 u does not have a sense.

To solve this problem arising from many experimental fields of science, where the second member u stems from measurements, we propose a recurrent procedure which converges almost completely and in quadratic mean to L-pseudo-solution and for which we build up a confidence interval. To check the validity of our results, a numerical example which is standard in rheology is proposed.

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Authors and Affiliations

  1. Lab. Math. Appl., University A. Mira, 06000, Bejaia, Algeria

    Abdelnasser Dahmani, Halima Zerouati & Fatah Bouhmila

Authors
  1. Abdelnasser Dahmani
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  2. Halima Zerouati
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  3. Fatah Bouhmila
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Correspondence to Abdelnasser Dahmani.

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Dahmani, A., Zerouati, H. & Bouhmila, F. The L-pseudo-solution using stochastic algorithm of Landweber. Meccanica 47, 1935–1943 (2012). https://doi.org/10.1007/s11012-012-9565-y

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  • DOI: https://doi.org/10.1007/s11012-012-9565-y

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