Regularisierung schlecht gestellter Probleme durch Projektionsverfahren

DOI10.1007/BF01389972zbMath0364.65042MaRDI QIDQ1241017

Frank Natterer

Publication date: 1977

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132491

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Numerical methods for integral equations (65R20)

Related Items (50)

Theory and the methods of solution of ill-posed problems ⋮ A study of regularization by monotonicity ⋮ On the stability of integral equations of the first kind with logarithmic kernels ⋮ Approximation of the solution to the moment problem in a hilbert space ⋮ Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization for ill–posed operator equations ⋮ On Self-regularization of Ill-Posed Problems in Banach Spaces by Projection Methods ⋮ The Galerkin scheme for Lavrentiev's \(m\)-times iterated method to solve linear accretive Volterra integral equations of the first kind ⋮ Greedy Tikhonov regularization for large linear ill-posed problems ⋮ Operator-theoretic and regularization approaches to ill-posed problems ⋮ On the regularization of projection methods for solving ill-posed problems ⋮ Approximate solutions for a finite moment problem ⋮ Numerical inversion of the Radon transform ⋮ An iterative method for Tikhonov regularization with a general linear regularization operator ⋮ Adaptive Spectral Inversion for inverse medium problems ⋮ Galerkin spectral method for a multi-term time-fractional diffusion equation and an application to inverse source problem ⋮ Quadratic Neural Networks for Solving Inverse Problems ⋮ Solution of ill-posed problems with Chebfun ⋮ Error bounds of discretization methods for boundary integral equations with noisy data ⋮ Convergence rates of a multilevel method for the regularization of nonlinear ill-posed problems ⋮ A numerical solver based on \(B\)-splines for 2D vector field tomography in a refracting medium ⋮ On the super-approximation property of Galerkin's method with finite elements ⋮ On the stability of the spline collocation method for a class of integral equations of the first kind ⋮ A numerical study of variable coefficient elliptic Cauchy problem via projection method ⋮ On a Family of Gradient-Type Projection Methods for Nonlinear Ill-Posed Problems ⋮ Incremental projection approach of regularization for inverse problems ⋮ Approximate inversion of the 3 D radon transform ⋮ General regularization schemes for signal detection in inverse problems ⋮ On the characterization of self-regularization properties of a fully discrete projection method for Symm's integral equation ⋮ Regularization by projection: Approximation theoretic aspects and distance functions ⋮ V-cycle convergence of some multigrid methods for ill-posed problems ⋮ On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations ⋮ Direct and inverse results in variable Hilbert scales ⋮ Regularization by projection in variable Hilbert scales ⋮ Fitting multidimensional data using gradient penalties and the sparse grid combination technique ⋮ A Variant of Projection-Regularization Method for Ill-Posed Linear Operator Equations ⋮ Smoothed projection methods for the moment problem ⋮ Bayesian inverse problems with non-commuting operators ⋮ Stability and robustness of collocation methods for Abel-type integral equations ⋮ Solving inverse problems using data-driven models ⋮ DETERMINATION OF PARAMETERS IN NONLINEAR HYPERBOLIC PDES VIA A MULTIHARMONIC FORMULATION, USED IN PIEZOELECTRIC MATERIAL CHARACTERIZATION ⋮ Toward Global Convergence for Strongly Nonlinear Ill-Posed Problems via a Regularizing Multilevel Approach ⋮ A convergence analysis of regularization by discretization in preimage space ⋮ Convergence Analysis of Pixel-Driven Radon and Fanbeam Transforms ⋮ Convergence Rates for Tikhonov Regularization in Finite-Dimensional Subspaces of Hilbert Scales ⋮ Error bounds for tikhonov regularization in hilbert scales ⋮ Ill-Posed Problems: Operator Methodologies of Resolution and Regularization ⋮ Thresholding projection estimators in functional linear models ⋮ DISCREPANCY SETS FOR COMBINED LEAST SQUARES PROJECTION AND TIKHONOV REGULARIZATION ⋮ On stochastic Kaczmarz type methods for solving large scale systems of ill-posed equations ⋮ Deep neural networks can stably solve high-dimensional, noisy, non-linear inverse problems

Cites Work

• Unnamed Item
• On the error estimate in the solution of equations of the first kind
• Numerical and asymptotic techniques in electromagnetics
• Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren
• A finite element method for some integral equations of the first kind
• Zur Konvergenz von Näherungsverfahren bezüglich verschiedener Normen. (On convergence of approximation methods with respect to various norms)
• A product integration method for a class of singular first kind Volterra equations
• A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
• On Tikhonov's Method for Ill-Posed Problems
• On the Equivalence of Regularization and Certain Reproducing Kernel Hilbert Space Approaches for Solving First Kind Problems
• Bounding the Error in Spline Interpolation
• Convergence Rates of Approximate Least Squares Solutions of Linear Integral and Operator Equations of the First Kind
• On the numerical solution of nonlinear Volterra integro-differential equations

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