Theory and the methods of solution of ill-posed problems

General theory of numerical analysis in abstract spaces (65J05) Numerical methods for integral equations (65R20) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Equations and inequalities involving linear operators, with vector unknowns (47A50)

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Asymptotic regularization for integral equations of the first kind

Cites Work

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The finite element method for ill-posed problems
Digital Removal of Random Media Image Degradations by Solving the Diffusion Equation Backwards in Time
Numerical Solution of Integral Equations of the First Kind with Nonsmooth Kernels
ON OPTIMAL ALGORITHMS FOR OPERATOR EQUATIONS OF THE FIRST KIND WITH A PERTURBED OPERATOR
Optimal Estimation of Linear Operators in Hilbert Spaces from Inaccurate Data
Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed Problems
An estimate of the error of the approximate solution obtained by a non-linear regularizing algorithm
Solution of convolution-type integral equations of the first kind in the multidimensional case
Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator Equations
On Error Bounds for Generalized Inverses
Statistical Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind
On the Approximate Minimization of Functionals
Perturbation theory for pseudo-inverses
Solution of some lexicographic problems of interpretation
On spline functions and statistical regularization of ill-posed problems
Difference approximation and regularization of optimal control problems for Goursat-Darboux systems
Measurability and regularizability of mappings inverse to continuous linear operators
An optimal method for approximating the values of nonlinear operators
Optimal methods of computing the values of the operator Ux if x is given with an error. Differentiation of functions defined with an error
Stable solution of operator equations of the first kind by the steepest- descent method
A problem of reconstructing a Riemannian metric
Multipurpose systems for comprehensive mathematical processing of spectrometric observations
On the solution of nonlinear equations with monotone operators in a Banach space
A finite element method for some integral equations of the first kind
A certain approach to the problem of regularization on the basis of the perturbation of linear operators
Regularisierung schlecht gestellter Probleme durch Projektionsverfahren
Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation
Some aspects of the behavior of regularized solutions as the amount of smoothing is varied
Nonconvergence results for the application of least-squares estimation to ill-posed problems
Method of monotonicity and approximate computation of the value of an unbounded nonlinear operator
Relationship of several variational methods for the approximate solution of ill-posed problems
A fast quadratic programming method for solving ill-conditioned systems of equations
Zur Regularisierung einer Klasse nichtkorrekter Probleme bei Evolutionsgleichungen. (On the regularization of a certain class of improperly posed problems for evolution equations)
On some problems of integral geometry
Numerical differentiation procedures for non-exact data
Best accessible estimation: Convergence properties and limiting forms of the direct and reduced versions
On the L\(_2\) improperly posed problems
On the Tikhonov-stable summation of Fourier series with perturbed coefficients by some regular methods
The construction of solutions to the heat equation backward in time
On uniqueness, stability and pointwise estimates in the Cauchy problem for coupled elliptic equations
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Adaptive Numerical Differentiation
Dimensionality Reduction Methods for Efficient Numerical Solution, Backward in Time, of Parabolic Equations with Variable Coefficients
Minimum Principles for Ill-Posed Problems
Construction of a normal solution of non-linear ill-posed problems by the method of regularization
Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
The axisymmetric cauchy problem for Laplace's equation
Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kind
On the stable differentiation of functions
The choice of the constant in a. a. tikhonov's rule for specifying the regularization parameter in the solution of linear conditionally well-posed problems
Convex lexicographic problems
Approximations to Generalized Inverses of Linear Operators
On Fredholm Integral Equations of the First Kind with Convex Constraints
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
THE DEVELOPMENTS OF MATHEMATICAL METHODS FOR THE STUDY OF DIRECT AND INVERSE PROBLEMS IN ELECTRODYNAMICS

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