Results 151 to 160 of about 5,632,119 (202)

Ill-Posed Problems

2013
As previously mentioned, for problems in mathematical physics Hadamard [95] postulated three requirements: a solution should exist, the solution should be unique, and the solution should depend continuously on the data. The third postulate is motivated by the fact that in all applications the data will be measured quantities.
Fioralba Cakoni, David Colton
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AN ILL-POSED PROBLEM FOR THE HEAT EQUATION

Mathematical Models and Methods in Applied Sciences, 2009
The Cauchy problem for the heat equation in which Cauchy data are prescribed on the outer boundary of a domain with cavity and no data are given on the inner boundary is known to be ill-posed. By a slight modification of the boundary conditions a new problem is introduced whose solution depends continuously on the data in L2.
Payne, L. E., Philippin, G. A.
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Stochastic Methods for Ill-Posed Problems

BIT Numerical Mathematics, 2000
This paper considers the behaviour of ill-posed problems of the stochastic Euler method, semi-implicit Euler method and some new method. The new method shows improved stability for stiff problems. It has been shown that the applied regularization cannot be driven beyond a certain critical parameter level.
Burrage, K., Piskarev, S.
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Optimal discretization of Ill-posed problems

Ukrainian Mathematical Journal, 2000
Summary: We present a review of results obtained in the Institute of Mathematics of National Ukrainian Academy of Sciences when investigating the optimal digitization of ill-posed problems.
Pereverzev, S. V., Solodkij, S. G.
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The feature-binding problem is an ill-posed problem

Trends in Cognitive Sciences, 2012
The binding problem arises when visual features (colour, orientation), said to be coded in independent brain modules, are to be integrated into unitary percepts. I argue that binding is an ill-posed problem, because those modules are now known to code jointly for multiple features, rendering the feature-binding issue moot.
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Inverse and Ill-Posed Problems $$\star $$

2018
When we evaluate the expression \({{\varvec{f}}} = A{{\varvec{u}}}\), where \({{\varvec{u}}}\) and \({{\varvec{f}}}\) are vectors and A is a matrix, we solve a direct or forward problem. Given A we can precisely calculate \({{\varvec{f}}}\) for any \({{\varvec{u}}}\).
Simon Širca, Martin Horvat
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Regularization of Discrete Ill-Posed Problems

BIT Numerical Mathematics, 2004
Discrete approximations \( A_n u_n = f_n \) of an ill-posed equation (1) \( Au = f \) with a linear compact operator \( A: X \to X \) in a Hilbert space \( X \) are considered. Here, \( A_n: X_n \to X_n \) is a linear bounded operator in a finite-dimensional Hilbert space \( X_n \), where \( \{X_n,r_n,p_n\} \) is a convergent and stable discrete ...
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A descent method for regularization of ill-posed problems

Optimization Methods and Software, 2005
In this paper, we describe an iterative algorithm, called descent-TCG, based on truncated conjugate gradients iterations to compute Tikhonov regularized solutions of linear ill-posed problems. The sequence of approximate solutions and regularization parameters, computed by the algorithm, is shown to decrease the value of the Tikhonov functional ...
ZAMA, FABIANA, LOLI PICCOLOMINI, ELENA
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Ill-posed problems

1987
This section is devoted to a preliminary discussion of the stability problem. We shall give a definition of ill-posed problems and sketch the main idea to restore stability in ill-
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Ill-Posed Problems

1983
Problems involving differential equations usually come in the following form: we are given an equation for the unknown function u, P(u) = f, on a domain Ω together with some “side” conditions on u. For example, we may require that u assumes certain preassigned values on ∂Ω, or that u is in L 2(Ω), or that u is in class C k in Ω.
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