Results 251 to 260 of about 413,861 (307)

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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The Ill-Posed Problem in DIC

2017
The contribution of our paper is to present a mixed finite element method for estimation of the velocity in the optical flow constraint, i.e., an advection equation. The resulting inverse problem is well-known to be undetermined because the velocity vector cannot be recovered from the scalar field advected unless further restrictions on the flow, or ...
Rich Lehoucq, Dan Turner
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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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Ill-posed problems in geomechanics

Journal of Mining Science, 2011
Any inverse problem requires that its ill-posedness be overcome through regularization or derivation of precise equations. On the basis of singular integral equations, connecting boundary values of stresses and displacements, the author proposes convergence method and its numerical algorithm in terms of a piecewise-homogeneous domain (pillar) where ...
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The Effect of the Ill-posed Problem on Quantitative Error Assessment in Digital Image Correlation

Experimental mechanics, 2017
R. Lehoucq, P. Reu, D. Turner
semanticscholar   +1 more source

On condition numbers and the distance to the nearest ill-posed problem

, 2015
J. Demmel
semanticscholar   +1 more source

On the computation of a truncated SVD of a large linear discrete ill-posed problem

Numerical Algorithms, 2017
Enyinda Onunwor, L. Reichel
semanticscholar   +1 more source