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Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration

Author

Listed:
  • Rong Zhang

    (School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China
    Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, China)

  • Fanchun Li

    (School of Social Management, Jiangxi College of Applied Technology, Ganzhou 341000, China)

  • Xingjun Luo

    (School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China)

Abstract

In this paper, Landweber iteration with a relaxation factor is proposed to solve nonlinear ill-posed integral equations. A compression multiscale Galerkin method that retains the properties of the Landweber iteration is used to discretize the Landweber iteration. This method leads to the optimal convergence rates under certain conditions. As a consequence, we propose a multiscale compression algorithm to solve nonlinear ill-posed integral equations. Finally, the theoretical analysis is verified by numerical results.

Suggested Citation

  • Rong Zhang & Fanchun Li & Xingjun Luo, 2020. "Multiscale Compression Algorithm for Solving Nonlinear Ill-Posed Integral Equations via Landweber Iteration," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:221-:d:318345
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