Results 1 to 10 of about 23,965 (163)
On the discrete linear ill‐posed problems
Mathematical Modelling and Analysis, 1999 An inverse problem of photo‐acoustic spectroscopy of semiconductors is investigated. The main problem is formulated as the integral equation of the first kind.
A. A. Stepanov
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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.
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Regularization of exponentially ill-posed problems
Numerical Functional Analysis and Optimization, 2000 Linear and nonlinear inverse problems which are exponentially ill-posed arise in heat conduction, satellite gradiometry, potential theory and scattering theory. For these problems logarithmic source conditions have natural interpretations whereas standard Holder-type source conditions are far too restrictive.
Thorsten Hohage
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Economic Cycles of Carnot Type
Entropy, 2021 Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a ...
Constantin Udriste +2 more
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Discrete and Continuous Models and Applied Computational Science, 2023 The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved.
Aleksandr A. Belov
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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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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. The 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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