DOI: https://doi.org/10.26089/NumMet.v21r430

On the method of calculating the modulus of continuity of the inverse operator and its modifications with application to non-linear problems of geoelectrics

Authors

  • M.I. Shimelevich

Keywords:

inverse problem
modulus of continuity of an operator
a priori and a posteriori estimates
Monte Carlo
geoelectrics

Abstract

The article considers a priori estimates of the ambiguity (error) of approximate solutions of conditionally correct nonlinear inverse problems based on the modulus of continuity of the inverse operator and its modifications. It is shown that in the class of piecewise constant solutions defined on a given parametrization grid, the modulus of continuity of the inverse operator and its modifications monotonously increase with increasing mesh dimension. A method is proposed for constructing an optimal parameterization grid that has a maximum dimension provided that the modulus of continuity of the inverse operator does not exceed a given value. A numerical algorithm for calculating the modulus of continuity of the inverse operator and its modifications using Monte Carlo algorithms is presented; questions of convergence of the algorithm are investigated. The proposed method is also applicable for calculating classical posterior error estimates. Numerical examples are given for nonlinear inverse problems of geoelectrics.

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Published

2020-11-03

Issue

Vol. 21 (2020): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biography

M.I. Shimelevich

Sergo Ordzhonikidze Russian State University for Geological Prospecting (MGRI)
Faculty of Geology and Geophysics of oil and gas
• Associate Professor

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