Optimality for ill-posed problems under general source conditions
From MaRDI portal
Publication:4400147
DOI10.1080/01630569808816834zbMath0907.65049OpenAlexW1966384449MaRDI QIDQ4400147
Publication date: 4 March 1999
Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/01630569808816834
numerical examplesHilbert spacesregularization methodsspectral methodsill-posed inverse problemTikhonov methods
Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)
Related Items
Reconstruction of a space-dependent source in the inexact order time-fractional diffusion equation ⋮ Fourier regularization method of a sideways heat equation for determining surface heat flux ⋮ An optimal method for fractional heat conduction problem backward in time ⋮ Optimal stable solution of Cauchy problems for elliptic equations ⋮ Lavrentiev regularization for linear ill-posed problems under general source conditions ⋮ Hölder-logarithmic type approximation for nonlinear backward parabolic equations connected with a pseudo-differential operator ⋮ Optimal stable approximation for the Cauchy problem for Laplace equation ⋮ The inverse source problem for time-fractional diffusion equation: stability analysis and regularization ⋮ Optimal error bound and Fourier regularization for identifying an unknown source in the heat equation ⋮ Spectral Galerkin method and its application to a Cauchy problem of Helmholtz equation ⋮ A regularization method for a Cauchy problem of the Helmholtz equation ⋮ An a posteriori mollification method for the heat equation backward in time ⋮ On a fractional backward heat conduction problem: application to deblurring ⋮ Regularizability of ill-posed problems and the modulus of continuity ⋮ Spectral method for ill-posed problems based on the balancing principle ⋮ Spectral regularization method for the time fractional inverse advection-dispersion equation ⋮ An improved error bound on the boundary inversion for a sideways heat equation ⋮ Numerical pseudodifferential operator and Fourier regularization ⋮ Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities ⋮ A note on a Cauchy problem for the Laplace equation: Regularization and error estimates ⋮ Two-parameter regularization method for a nonlinear backward heat problem with a conformable derivative ⋮ A linear regularization method for a nonlinear parameter identification problem ⋮ Stabilizing the nonlinear spherically symmetric backward heat equation via two-parameter regularization method ⋮ Optimal error bound and truncation regularization method for a backward time-fractional diffusion problem in Hilbert scales ⋮ Regularization technique for an inverse space-fractional backward heat conduction problem ⋮ On Tikhonov's method and optimal error bound for inverse source problem for a time-fractional diffusion equation ⋮ A posteriori regularization parameter choice rule for a modified kernel method for a time-fractional inverse diffusion problem ⋮ Regularization methods for a problem of analytic continuation ⋮ Quadrature based collocation methods for integral equations of the first kind ⋮ A mollification method for backward time-fractional heat equation ⋮ An optimal filtering method for the Cauchy problem of the Helmholtz equation ⋮ Approximate inverse method for stable analytic continuation in a strip domain ⋮ Shannon wavelet regularization methods for a backward heat equation ⋮ An inverse problem for fractional diffusion equation in 2-dimensional case: stability analysis and regularization ⋮ Nonlinear wavelet methods for high-dimensional backward heat equation ⋮ A regularization method for solving the Cauchy problem for the Helmholtz equation ⋮ A variational technique of mollification applied to backward heat conduction problems ⋮ On regularization and error estimates for the backward heat conduction problem with time-dependent thermal diffusivity factor ⋮ An inverse problem for a fractional diffusion equation ⋮ ERROR ESTIMATES ON A BACKWARD HEAT EQUATION BY A WAVELET DUAL LEAST SQUARES METHOD ⋮ A wavelet method for the Cauchy problem for the Helmholtz equation ⋮ Posterior consistency of nonparametric conditional moment restricted models ⋮ Optimal error bound and modified kernel method for a space-fractional backward diffusion problem ⋮ Two iterative methods for a Cauchy problem of the elliptic equation with variable coefficients in a strip region ⋮ A mollification regularization method for a fractional-diffusion inverse heat conduction problem ⋮ Two numerical methods for a Cauchy problem for modified Helmholtz equation ⋮ Notes on a new approximate solution of 2-D heat equation backward in time ⋮ Modulus of continuity for conditionally stable ill-posed problems in Hilbert space ⋮ Convergence of the Hilbert uniqueness method via Tikhonov regularization ⋮ A non-local boundary value problem method for parabolic equations backward in time ⋮ The truncation method for identifying the heat source dependent on a spatial variable ⋮ An optimal regularization method for space-fractional backward diffusion problem ⋮ A Hermite extension method for numerical differentiation ⋮ On the ill-posed analytic continuation problem: an order optimal regularization scheme ⋮ Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation ⋮ Optimal error bound in a Sobolev space of regularized approximation solutions for a sideways parabolic equation ⋮ Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions ⋮ OPTIMAL ERROR BOUND AND APPROXIMATION METHODS FOR A CAUCHY PROBLEM OF THE MODIFIED HELMHOLTZ EQUATION ⋮ On the axisymmetric backward heat equation with non-zero right hand side: regularization and error estimates ⋮ A simple regularization method for the ill-posed evolution equation ⋮ Stability results for semi-linear parabolic equations backward in time ⋮ Two-parameter regularization method for an axisymmetric inverse heat problem ⋮ Some novel linear regularization methods for a deblurring problem ⋮ ON RATE OPTIMALITY FOR ILL-POSED INVERSE PROBLEMS IN ECONOMETRICS ⋮ ESTIMATION OF A SEMIPARAMETRIC IGARCH(1,1) MODEL ⋮ Stability estimate and regularization for a radially symmetric inverse heat conduction problem ⋮ Regularization for a fractional sideways heat equation ⋮ On the a posteriori choice of a regularization parameter in the solution of severely ill-posed problems ⋮ Numerical reconstruction of a non-smooth heat flux in the inverse radial heat conduction problem ⋮ Wavelet and spectral regularization methods for a sideways parabolic equation ⋮ A mollification regularization method for stable analytic continuation ⋮ Optimal regularization for an unknown source of space-fractional diffusion equation ⋮ An order optimal regularization method for the Cauchy problem of a Laplace equation in an annulus domain ⋮ Optimal modified method for a fractional-diffusion inverse heat conduction problem ⋮ Sharp estimates for approximations to a nonlinear backward heat equation ⋮ The Fourier regularization for solving the Cauchy problem for the Helmholtz equation ⋮ A \textit{a posteriori} regularization for the Cauchy problem for the Helmholtz equation with inhomogeneous Neumann data ⋮ Backward problem for time-space fractional diffusion equations in Hilbert scales ⋮ Identifying an unknown source term in a time-space fractional parabolic equation ⋮ On a weighted time-fractional asymptotical regularization method ⋮ A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case ⋮ The revised generalized Tikhonov regularization for the inverse time-dependent heat source problem ⋮ Regularization in Banach spaces — convergence rates by approximative source conditions ⋮ Wavelet regularization strategy for the fractional inverse diffusion problem ⋮ Spectral regularization methods for solving a sideways parabolic equation within the framework of regularization theory ⋮ On optimization of projection methods for solving some classes of severely ill-posed problems ⋮ ON MOROZOV’S DISCREPANCY PRINCIPLE FOR NONLINEAR ILL-POSED EQUATIONS ⋮ A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations ⋮ A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation ⋮ Identifying an unknown source term in a heat equation ⋮ Conditional Stability Estimates and Regularization with Applications to Cauchy Problems for the Helmholtz Equation ⋮ Hyperbolic cross and the complexity of various classes of ill-posed linear problems ⋮ Numerical differentiation from a viewpoint of regularization theory ⋮ Landweber iteration regularization method for identifying unknown source on a columnar symmetric domain ⋮ On optimal regularization methods for fractional differentiation ⋮ General Source Conditions for Nonlinear Ill-Posed Equations ⋮ The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations ⋮ Regularization methods for identifying the initial value of time fractional pseudo-parabolic equation ⋮ Numerical solution of a 2D inverse heat conduction problem ⋮ Three regularization methods for identifying the initial value of time fractional advection-dispersion equation ⋮ Unknown source identification problem for space-time fractional diffusion equation: optimal error bound analysis and regularization method ⋮ Morozov's discrepancy principle for tikhonov ⋮ On the analysis of distance functions for linear ill-posed problems with an application to the integration operator inL2 ⋮ Regularization of ill-posed problems involving constant-coefficient pseudo-differential operators ⋮ A new generalized Tikhonov method based on filtering idea for stable analytic continuation ⋮ Backward semi-linear parabolic equations with time-dependent coefficients and local Lipschitz source ⋮ Analysis of the discrepancy principle for Tikhonov regularization with oversmoothing penalty term under low order source conditions ⋮ On regularization results for a two-dimensional nonlinear time-fractional inverse diffusion problem ⋮ Identifying a space-dependent source term in distributed order time-fractional diffusion equations ⋮ A Source Identification Problem in a Bi-parabolic Equation: Convergence Rates and Some Optimal Results ⋮ An iterative method based on Nesterov acceleration for identifying space-dependent source term in a time-fractional diffusion-wave equation ⋮ Regularization of the inverse Laplace transform by mollification ⋮ An Inverse Diffraction Problem: Shape Reconstruction ⋮ Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule ⋮ Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation ⋮ Determination of the unknown source term in a space-fractional diffusion equation ⋮ Fourier regularization method for solving a Cauchy problem for the Laplace equation ⋮ An inverse problem for space‐fractional backward diffusion problem ⋮ A generalization of continuous regularized Gauss–Newton method for ill-posed problems ⋮ Range Inclusions and Approximate Source Conditions with General Benchmark Functions ⋮ Tikhonov regularization of nonlinear ill-posed equations under general source condition ⋮ Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework ⋮ Stability results for backward time-fractional parabolic equations ⋮ Convergence rates for Tikhonov regularization from different kinds of smoothness conditions ⋮ An optimal quasi solution for the Cauchy problem for Laplace equation in the framework of inverse ECG ⋮ A non-local boundary value problem method for semi-linear parabolic equations backward in time ⋮ A spectral method for an axisymmetric backward heat equation ⋮ An optimal modified method for a two-dimensional inverse heat conduction problem ⋮ A potential-free field inverse Schrödinger problem: optimal error bound analysis and regularization method ⋮ Linear estimates of accuracy for approximate solutions of inverse problems ⋮ COMPLEXITY ESTIMATES FOR SEVERELY ILL-POSED PROBLEMS UNDER A POSTERIORI SELECTION OF REGULARIZATION PARAMETER ⋮ Regularization of exponentially ill-posed problems
Cites Work
- On a minimax equality for seminorms
- Optimal Estimation of Linear Operators in Hilbert Spaces from Inaccurate Data
- Tikhonov Regularization for Finitely and Infinitely Smoothing Operators
- Optimal Filtering for the Backward Heat Equation
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item