LAVRENTIEV REGULARIZATION OF NONLINEAR ILL-POSED EQUATIONS UNDER GENERAL SOURCE CONDITION

Authors

  • P. Mahale Department of Mathematics, I.I.T. Madras, Chennai 600036, India
  • M. Nair Department of Mathematics, I.I.T. Madras, Chennai 600036, India

Abstract

Analogues to the procedure adopted by Scherzer et.al (1993) for choosing the regularization parameter in Tikhonov regularization of nonlinear ill-posed equations of the form F(x) = y, Tautenhahn (2002) considered an a posteriori parameter choice strategy for Lavrentiev regularization, and derived order optimal error estimates under Holder type source conditions. In this paper, we derive order optimal error estimates under a general source condition so that the results are applicable for both mildly and exponentially ill-posed problems. Results in this paper generalize results of Tautenhahn (2002) and also extend results of Nair and Tautenhahn (2004) to the nonlinear case.

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Published

2013-10-27

How to Cite

Mahale, P., & Nair, M. (2013). LAVRENTIEV REGULARIZATION OF NONLINEAR ILL-POSED EQUATIONS UNDER GENERAL SOURCE CONDITION. Journal of Nonlinear Analysis and Optimization: Theory & Applications, 4(2), 193-204. Retrieved from http://www.math.sci.nu.ac.th/ojs302/index.php/jnao/article/view/186

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Section

Research Article