Results 81 to 90 of about 26,359 (120)

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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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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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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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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Noise Models for Ill-Posed Problems

2010
The standard view of noise in ill-posed problems is that it is either deterministic and small (strongly bounded noise) or random and large (not necessarily small). Following Eggerment, LaRiccia and Nashed (2009), a new noise model is investigated, wherein the noise is weakly bounded.
Eggermont, Paul N., LaRiccia, Vincent, Nashed, M. Zuhair   +2 more
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A Regularization Parameter in Discrete Ill-Posed Problems

SIAM Journal on Scientific Computing, 1996
The author considers the Tikhonov regularization method for the discrete ill-posed problem of minimizing \[ J_\alpha(u)=|Ku-f|^2+\alpha|u|^2, \] where \(K\) is an \(m\times n\) matrix with a large condition number, \(m\geq n\), and \(\alpha>0\). The Euclidean norm is used.
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Ill-posed problems in rheology

Rheologica Acta, 1989
Experimental data are always noisy and often incomplete. This leads to ambiguities if one wants to infer from the data some functions, which are related to the measured quantity through an integral equation of the first kind. In rheology many of such so-called ill-posed problems appear.
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Spectroscopy; An Ill-Posed Problem

SPIE Proceedings, 1985
Spectroscopy can be described as an inversion technique for the retrieval from measured data of an unknown spectral distribution. The implications which follow from this general approach are discussed. It turns out that spectroscopy belongs to the category of ill-posed problems that have more degrees of freedom than data.
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