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The residual method for regularizing ill-posed problems.
Appl Math Comput, 2011 Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years.
Grasmair M, Haltmeier M, Scherzer O.
europepmc +4 more sources
RUDN Journal of Informatization in Education, 2020 Problem and goal. Computer technologies are now widely used in applied research aimed at obtaining new scientific knowledge. These studies used the method of computer modeling and computing experiment, from which it is possible to study the properties of
Viktor S. Kornilov
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Numerical Methods for Ill-Posed, Linear Problems [PDF]
, 1975 A means of assessing the effectiveness of methods used in the numerical solution of various linear ill-posed problems is outlined. Two methods: Tikhonov' s method of regularization and the quasireversibility method of Lattès and Lions are appraised from ...
Stevens, Thomas
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Ill-posed problems in thermomechanics
Applied Mathematics Letters, 2009 Several thermomechanical models have been proposed from a heuristic point of view. A mathematical analysis should help to clarify the applicability of these models, among those recent thermal or viscoelastic models. Single-phase-lag and dual-phase-lag heat conduction models can be interpreted as formal expansions of delay equations.
Michael Dreher +2 more
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Regularization technique and numerical analysis of the mixed system of first and second-kind Volterra–Fredholm integral equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 It is important to note that mixed systems of first and second-kind Volterra–Fredholm integral equations are ill-posed problems, so that solving discretized system of such problems has a lot of difficulties.
S. Pishbin, J. Shokri
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Solving ill-posed Helmholtz problems with physics-informed neural networks
Journal of Numerical Analysis and Approximation Theory, 2023 We consider the unique continuation (data assimilation) problem for the Helmholtz equation and study its numerical approximation based on physics-informed neural networks (PINNs).
Mihai Nechita
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Solution of ill-posed problems with Chebfun
Numerical Algorithms, 2022 AbstractThe analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. However, the numerical solution of these problems typically is computed by first discretizing the problem and then applying tools from finite-dimensional linear algebra.
Abdulaziz Alqahtani +2 more
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On Tikhonov's Method for Ill-Posed Problems [PDF]
Mathematics of Computation, 1974 For Tikhonov’s regularization of ill-posed linear integral equations, numerical accuracy is estimated by a modulus of convergence, for which upper and lower bounds are obtained. Applications are made to the backward heat equation, to harmonic continuation, and to numerical differentiation.
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Optimisation in the regularisation ill-posed problems [PDF]
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1986 We survey the role played by optimization in the choice of parameters for Tikhonov regularization of first-kind integral equations. Asymptotic analyses are presented for a selection of practical optimizing methods applied to a model deconvolution problem. These methods include the discrepancy principle, cross-validation and maximum likelihood.
Davies, A. R., Anderssen, R. S.
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Theoretical and Experimental Heat Transfer in Solid Propellant Rocket Engine [PDF]
Journal of Aerospace Technology and Management, 2019 Accurate determination of heat flux is an important task not only in the designing aspect but also in the performance analysis of rocket engines. In this purpose, this work deals with the heat flux determination in a combustion chamber through the ...
Izabel Cecilia Ferreira de Souza Vicentin +7 more
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