A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations

DOI10.1142/S0219876221500080OpenAlexW3089551557MaRDI QIDQ3383910

Boussetila Nadjib, Bechouat Tahar, Rebbani Faouzia

Publication date: 16 December 2021

Published in: International Journal of Computational Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219876221500080

zbMATH Keywords

Tikhonov regularizationill-posed problemsfirst kind Fredholm integral equationsfinite rank approximation

Mathematics Subject Classification ID

Operator theory (47-XX) Numerical analysis (65-XX)

Related Items (3)

Numerical solution of the two-dimensional first kind Fredholm integral equations using a regularized collocation method ⋮ A COLLOCATION METHOD FOR FREDHOLM INTEGRAL EQUATIONS OF THE FIRST KIND VIA ITERATIVE REGULARIZATION SCHEME ⋮ Jacobi spectral projection methods for Fredholm integral equations of the first kind

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Projection methods for ill-posed problems revisited
• Projected Tikhonov regularization method for Fredholm integral equations of the first kind
• Regularization theory for ill-posed problems. Selected topics
• A posteriori parameter choice strategy for fast multiscale methods solving ill-posed integral equations
• Discrete Legendre spectral projection methods for Fredholm-Hammerstein integral equations
• Convergence analysis of Legendre spectral projection methods for Hammerstein integral equations of mixed type
• Multiscale Galerkin methods for the nonstationary iterated Tikhonov method with a modified posteriori parameter selection
• Direct and inverse results in variable Hilbert scales
• A parameter choice strategy for a multi-level augmentation method solving ill-posed operator equations
• Cubically convergent methods for selecting the regularization parameters in linear inverse problems
• Analysis of approximation methods for differential and integral equations
• Discrepancy principles for Tikhonov regularization of ill-posed problems leading to optimal convergence rates
• A variant of finite-dimensional Tikhonov regularization with a-posteriori parameter choice
• On the regularization of projection methods for solving ill-posed problems
• Regularization of ill-posed problems: Optimal parameter choice in finite dimensions
• Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
• A trigonometrical approach for some projection methods
• A discrete regularization method for ill-posed operator equations
• Regularization of discrete ill-posed problems
• Convergence analysis of a regularized approximation for solving Fredholm integral equations of the first kind
• A modified convergence analysis for solving Fredholm integral equations of the first kind
• Optimization of projection methods for solving ill-posed problems
• On the parameter choice in the multilevel augmentation method
• A family of rules for parameter choice in Tikhonov regularization of ill-posed problems with inexact noise level
• Regularized collocation method for Fredholm integral equations of the first kind
• A fast multiscale Galerkin method for the first kind ill-posed integral equations via iterated regularization
• Optimal Discretization of Inverse Problems in Hilbert Scales. Regularization and Self-Regularization of Projection Methods
• A convergence analysis of regularization by discretization in preimage space
• Two-parameter discrepancy principle for combined projection and Tikhonov regularization of ill-posed problems
• A parameter choice strategy for the regularized approximation of Fredholm integral equations of the first kind
• Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
• Multiscale collocation methods for ill-posed integral equations via a coupled system
• A multilevel augmentation method for solving ill-posed operator equations
• Role of Hilbert Scales in Regularization Theory
• Analysis of Profile Functions for General Linear Regularization Methods
• Finite-Dimensional Approximation Settings for Infinite-dimensional Moore–Penrose Inverses
• Asymptotic convergence rate of arcangeli's method for III-posed problems
• Iterative choices of regularization parameters in linear inverse problems
• A discrepancy principle for Tikhonov regularization with approximately specified data
• Optimality for ill-posed problems under general source conditions
• Geometry of linear ill-posed problems in variable Hilbert scales
• Regularization of exponentially ill-posed problems
• A finite dimensional realization of the mollifier method for compact operator equations
• Wavelet-Galerkin methods for ill-posed problems
• Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems
• Variable hilbert scales and their interpolation inequalities with applications to tikhonov regularization
• ON THE SELF-REGULARIZATION OF ILL-POSED PROBLEMS BY THE LEAST ERROR PROJECTION METHOD
• DISCREPANCY SETS FOR COMBINED LEAST SQUARES PROJECTION AND TIKHONOV REGULARIZATION
• Multiscale Methods for Fredholm Integral Equations
• Arbitrary divergence speed of the least-squares method in infinite-dimensional inverse ill-posed problems
• Regularization by projection in variable Hilbert scales
• Spectral Methods
• Linear integral equations
• An introduction to the mathematical theory of inverse problems

This page was built for publication: A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations