1. New Trends in Applying LRM to Nonlinear Ill-Posed Equations.
- Author
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George, Santhosh, Sadananda, Ramya, Padikkal, Jidesh, Kunnarath, Ajil, and Argyros, Ioannis K.
- Subjects
MONOTONE operators ,NONLINEAR equations ,NONLINEAR operators ,HILBERT space ,GRAVIMETRY - Abstract
Tautenhahn (2002) studied the Lavrentiev regularization method (LRM) to approximate a stable solution for the ill-posed nonlinear equation κ (u) = v , where κ : D (κ) ⊆ X ⟶ X is a nonlinear monotone operator and X is a Hilbert space. The operator in the example used in Tautenhahn's paper was not a monotone operator. So, the following question arises. Can we use LRM for ill-posed nonlinear equations when the involved operator is not monotone? This paper provides a sufficient condition to employ the Lavrentiev regularization technique to such equations whenever the operator involved is non-monotone. Under certain assumptions, the error analysis and adaptive parameter choice strategy for the method are discussed. Moreover, the developed theory is applied to two well-known ill-posed problems—inverse gravimetry and growth law problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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