Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space
From MaRDI portal
Publication:2957531
DOI10.1088/0266-5611/32/12/125003zbMath1368.47044arXiv1607.05737OpenAlexW3106091815MaRDI QIDQ2957531
Publication date: 26 January 2017
Published in: Inverse Problems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.05737
singular perturbationconditional stabilitymonotone operatorsLavrentiev regularizationHölder and logarithmic convergence rateslinear and nonlinear operator equation in Hilbert spacelocal ill-posedness
Monotone operators and generalizations (47H05) Nonlinear ill-posed problems (47J06) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
On ill-posedness concepts, stable solvability and saturation, A Regularization Approach for an Inverse Source Problem in Elliptic Systems from Single Cauchy Data, A regularized variational inequality approach for nonlinear monotone ill-posed equations, Direct regularization for system of integral-algebraic equations of index-1
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Lavrentiev's regularization method in Hilbert spaces revisited
- Regularization methods in Banach spaces.
- An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems
- Lavrentiev regularization for linear ill-posed problems under general source conditions
- Expanding the applicability of Lavrentiev regularization methods for ill-posed problems
- Operator theoretic treatment of linear Abel integral equations of first kind
- Time-fractional diffusion equation in the fractional Sobolev spaces
- Lavrentiev regularization and balancing principle for solving ill-posed problems with monotone operators
- The index function and Tikhonov regularization for ill-posed problems
- On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems
- Sharp converse results for the regularization error using distance functions
- Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
- Analysis of Profile Functions for General Linear Regularization Methods
- Approximate source conditions for nonlinear ill-posed problems—chances and limitations
- Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
- Factors influencing the ill-posedness of nonlinear problems
- On the method of Lavrentiev regularization for nonlinear ill-posed problems
- One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization
- Generalized Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
- Range Inclusions and Approximate Source Conditions with General Benchmark Functions
- A note on logarithmic convergence rates for nonlinear Tikhonov regularization
- How general are general source conditions?
- Approximate source conditions in Tikhonov–Phillips regularization and consequences for inverse problems with multiplication operators
- Regularizing Newton--Kaczmarz Methods for Nonlinear Ill-Posed Problems
- Verification of a variational source condition for acoustic inverse medium scattering problems
- Convex analysis and monotone operator theory in Hilbert spaces