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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 263–270 (Mi timm1279)  
This article is cited in 6 scientific papers (total in 6 papers)

On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind

V. P. Tanana, A. I. Sidikova

South Ural State University, Chelyabinsk
Full-text PDF (139 kB) Citations (6)
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Abstract: A regularizing algorithm for the approximate solution of integral equations of the first kind is investigated. The algorithm involves a finite-dimensional approximation of the problem; more exactly, the integral equation is discretized in two variables. An error estimate of the algorithm is obtained with the use of the equivalence of the generalized discrepancy method and the generalized discrepancy principle.
Keywords: regularization, error estimate, ill-posed problem.
Received: 26.02.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 299, Issue 1, Pages 217–224
DOI: https://doi.org/10.1134/S0081543817090231
Bibliographic databases:
Document Type: Article
UDC: 517.948
Language: Russian
Citation: V. P. Tanana, A. I. Sidikova, “On estimating the error of an approximate solution caused by the discretization of an integral equation of the first kind”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 263–270; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 217–224
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm1279
  • https://www.mathnet.ru/eng/timm/v22/i1/p263
    • This publication is cited in the following 6 articles:
    1. H.K. Al-Mahdawi, Farah Hatem Khorsheed, Ali Subhi Alhumaima, Ali J. Ramadhan, Kilan M Hussien, Hussein Alkattan, N. Aldahan, A.J. Ramadhan, “Intelligent Particle Swarm Optimization Method for Parameter Selecting in Regularization Method for Integral Equation”, BIO Web Conf., 97 (2024), 00039  crossref
    2. H. K. Al-Mahdawi, Zainalabideen Albadran, Hussein Alkattan, Mostafa Abotaleb, Khder Alakkari, Ali J. Ramadhan, 4TH INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2022), 2977, 4TH INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2022), 2023, 020019  crossref
    3. Salam Abdulkhaleq Noaman, H.K. Al-Mahdawi, Bashar Talib Al-Nuaimi, A.I. Sidikova, “Iterative method for solving linear operator equation of the first kind”, MethodsX, 10 (2023), 102210  crossref
    4. H K Al-Mahdawi, “Development the Numerical Method to Solve the Inverse Initial Value Problem for the Thermal Conductivity Equation of Composite Materials”, J. Phys.: Conf. Ser., 1879:3 (2021), 032016  crossref
    5. H.K. Al-Mahdawi, “Development the Regularization Computing Method for Solving Boundary Value Problem to Heat Equation in the Composite Materials”, J. Phys.: Conf. Ser., 1999:1 (2021), 012136  crossref
    6. H K Al-Mahdawi, “Solving of an Inverse Boundary Value Problem for the Heat Conduction Equation by Using Lavrentiev Regularization Method”, J. Phys.: Conf. Ser., 1715:1 (2021), 012032  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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