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

PALLAVI  MAHALE; M. THAMBAN  NAIR

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

Authors

PALLAVI MAHALE Department of Mathematics, I.I.T. Madras, Chennai 600036, India
M. THAMBAN NAIR Department of Mathematics, I.I.T. Madras, Chennai 600036, India

Keywords:

Lavrentiev regularization, Inverse problems, Ill-posed problems, Discrepancy principle, Monotone operator

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.