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A. L. Ageev, T. V. Antonova, V. V. Vasin, E. A. Pimo- nov and F. J. Kuchuk, “Modified Levenberg-Marquardt Method for Deconvolution Problem Solution,” Youth International Scientific School-Conference “Theory and Numerical Methods for Solution of Inverse and Ill-Posed Problems”, Novosibirsk, 10-20 August 2009, Book of Abstracts, pp. 13-15. (in Russian)

has been cited by the following article:

• TITLE: New Regularization Algorithms for Solving the Deconvolution Problem in Well Test Data Interpretation

  AUTHORS: Vladimir Vasin, Georgy Skorik, Evgeny Pimonov, Fikri Kuchuk

  KEYWORDS: Deconvolution Problem, Volterra Equations, Well Test, Regularization Algorithm, Quasi-Solutions Method, Tikhonov Regularization, A Priori Information, Discrete Approximation, Non-Quadratic Stabilizing Functional, Special Basis

  JOURNAL NAME: Applied Mathematics, Vol.1 No.5, November 30, 2010

  ABSTRACT: Two new regularization algorithms for solving the first-kind Volterra integral equation, which describes the pressure-rate deconvolution problem in well test data interpretation, are developed in this paper. The main features of the problem are the strong nonuniform scale of the solution and large errors (up to 15%) in the input data. In both algorithms, the solution is represented as decomposition on special basic functions, which satisfy given a priori information on solution, and this idea allow us significantly to improve the quality of approximate solution and simplify solving the minimization problem. The theoretical details of the algorithms, as well as the results of numerical experiments for proving robustness of the algorithms, are presented.