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A Well-Posed Logarithmic Counterpart of an Ill-Posed Cauchy Problem
In this short paper, we study a well-posed logarithmic counterpart of an ill-posed Cauchy problem associated with an abstract evolution equation of...
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What Is an Inverse and Ill-Posed Problem?
In an inverse problem we draw conclusions about the cause from its observed (measured) effect. This kind of task is typically ill-posed, that is,...
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Solutions of An Ill-Posed Stefan Problem
We study the multi-phase Stefan problem with increasing Riemann initial data and generally negative latent specific heats for phase transitions. We...
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An Implicit Iteration Method for Solving Linear Ill-Posed Operator Equations
AbstractIn this work, we study a new implicit method to computing the solutions of ill-posed linear operator equations of the first kind under the...
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Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems
The growing availability and usage of low precision floating point formats attracts many interests of develo** lower or mixed precision algorithms...
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The Regularized Block GMERR Method and Its Simpler Version for Solving Large-Scale Linear Discrete Ill-Posed Problems
Based on the block Arnoldi process and minimizing the Frobenius norm of the error, the block generalized minimal error (GMERR) method and its simpler...
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Improved Accuracy Estimation of the Tikhonov Method for Ill-Posed Optimization Problems in Hilbert Space
AbstractThe Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional. Assuming that the sought...
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Regularization Methods for Ill-Posed Problems in Quantum Optics
On the example of the specific physical problem of noise reduction associated with losses, dark counts, and background radiation, in the statistics...
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Regularization of Linear Ill-Posed Problems in Hilbert Spaces
Let X and Y be Hilbert spaces. Further, let $$T\in...
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On the Equivalence of Singular and Ill-Posed Problems: The p-Factor Regularization Method
AbstractThe local equivalence of singular and ill-posed problems in a class of sufficiently smooth map**s is shown, which justifies the use of the p ...
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Deep Learning for Ill Posed Inverse Problems in Medical Imaging
Recently, with the significant developments in deep learning (DL) techniques, solving underdetermined inverse problems has become one of the major...
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A modified iterative Lavrentiev method for nonlinear monotone ill-posed operators
In this paper, we consider an iterative scheme for solving nonlinear ill-posed operator equations of monotone types under minimal and weaker...
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Estimate of the Spectrum of Discrete Sequences in Ill-Posed Problems Based on the Study of the Numerical Rank of the Trajectory Matrix
In this paper, we discuss properties of the singular value decomposition (SVD-decomposition) within the framework of the analysis of the numerical...
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Newton-Like Solvers for Non-linear Ill-Posed Problems
Let F : D(F) ⊂ X → Y act continuously Fréchet-differentiable between the Hilbert spaces X and Y . We like to solve...
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Solving Ill-Posed Problems of the Theory of Elasticity Using High-Performance Computing Systems
A method for the efficient analysis and solution of conditionally well-posed problems with a unique solution in the subspace is proposed. The use of...
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Modified version of a simplified Landweber iterative method for nonlinear ill-posed operator equations
In this paper, we consider a modified version of the simplified Landweber iterative regularization method which require calculation of the Frèchet...
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Gravimetry as an Ill-Posed Inverse Problem
This chapter discusses inverse gravimetry as an ill-posed problem in Newtonian potential theory. It is shown that all criteria of Hadamard’s...
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Tensor Arnoldi–Tikhonov and GMRES-Type Methods for Ill-Posed Problems with a t-Product Structure
This paper describes solution methods for linear discrete ill-posed problems defined by third order tensors and the t-product formalism introduced in...
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On the acceleration of optimal regularization algorithms for linear ill-posed inverse problems
Accelerated regularization algorithms for ill-posed problems have received much attention from researchers of inverse problems since the 1980s. The...
