Results 121 to 130 of about 23,965 (163)

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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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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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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Ill-Posed Problems and Regularization

1998
Click on the DOI link to access the article (may not be free). ; In this chapter, we consider the equation.
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Ill-Posed Problems of Geomechanics

Journal of Mining Science, 2018
The classical solution of elasticity problem on deformation of a plane weakened by a mathematical cut under wedging by constant forces is analyzed. The ill-posedness of the classical failure mechanics statements for problems with angular points is demonstrated.
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Ill-posed problems in mechanics

Mechanics of Solids, 2016
The notion of ill-posed initial and boundary value problems for partial differential equations was introduced by Hadamard, who also presented the first example of an ill-posed problem for a specific partial differential equation. At the same time, there are numerous examples of ill-posed problems in any field of mechanics.
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