Weighted Lavrentiev Regularization Method for Ill-posed Equations: Finite Dimensional Realization

Authors

  • Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka
  • K Kanagaraj Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA deemed to be University
  • Shubha V S Department of Mathematics, St Joseph Engineering College

Keywords:

ill-posed problem, simplified regularization, optimal order, finite dimensional realization, adaptive parameter choice strategy

Abstract

In this paper, we study weighted Lavrentiev regularization method for illposed operator equations in the finite dimensional subspaces of a Hilbert space. Using general Holder type source condition we obtain an optimal order error estimate. Adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) is used for choosing the regularization parameter. We applied the proposed method to an academic example to test the validity of theoretical result.

Author Biographies

Santhosh George, Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka

Professor of Mathematics at Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka - 575 025, India

K Kanagaraj, Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA deemed to be University

Associate Professor at Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA deemed to be University, Kumbakonam - 612 001, India

Shubha V S, Department of Mathematics, St Joseph Engineering College

Assistant Professor at Department of Mathematics, St Joseph Engineering College, Mangaluru -575 028, India

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Published

2022-12-09

How to Cite

George, S., Kanagaraj, K., & S, S. V. (2022). Weighted Lavrentiev Regularization Method for Ill-posed Equations: Finite Dimensional Realization. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(2), 201–210. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/87

Issue

Vol. 1 No. 2 (2022): July - December, 2022

Section

Articles

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Copyright (c) 2022 Santhosh George, K Kanagaraj, Shubha V S

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