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New Trends in Applying LRM to Nonlinear Ill-Posed Equations.
- Source :
- Mathematics (2227-7390); Aug2024, Vol. 12 Issue 15, p2377, 19p
- Publication Year :
- 2024
-
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]
- Subjects :
- MONOTONE operators
NONLINEAR equations
NONLINEAR operators
HILBERT space
GRAVIMETRY
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 12
- Issue :
- 15
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 178948997
- Full Text :
- https://doi.org/10.3390/math12152377