Results 11 to 20 of about 5,632,119 (202)
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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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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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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GPR prospecting in a layered medium via microwave tomography
Annals of Geophysics, 2003 The tomographic approach appears to be a promising way to elaborate Ground Penetrating Radar (GPR) data in order to achieve quantitative information on the tested regions.
F. Soldovieri, L. Crocco
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A comparison of regularizations for an ill-posed problem [PDF]
Mathematics of Computation, 1998 We consider numerical methods for a “quasi-boundary value” regularization of the backward parabolic problem given by \[ {
Karen A. Ames +3 more
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Approximation of Bayesian inverse problems for PDEs [PDF]
, 2010 Inverse problems are often ill posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability.
Dashti, Massoumeh +7 more
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Regularization of Linear Ill-Posed Problems involving Multiplication Operators
, 2020 We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function.
Mathé, Peter +2 more
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Self-regularization of projection methods with a posteriori discretization level choice for severely ill-posed problems [PDF]
, 2002 It is well known that projection schemes for certain linear ill-posed problems A퓍 = y can be regularized by a proper choice of the discretization level only, where no additional regularization is needed.
Bruckner, Gottfried +1 more
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