Displaying similar documents to “Compression of satellite data.”

Error autocorrection in rational approximation and interval estimates. [A survey of results.]

Grigori Litvinov (2003)

Open Mathematics

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The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates (in the framework of interval analysis including the so-called a posteriori interval analysis of Yu. Matijasevich) are too pessimistic. We shall discuss a very strong form of the effect which appears in rational approximations to functions. The error autocorrection...

A posteriori error control for the Allen–Cahn problem : circumventing Gronwall’s inequality

Daniel Kessler, Ricardo H. Nochetto, Alfred Schmidt (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Phase-field models, the simplest of which is Allen–Cahn’s problem, are characterized by a small parameter ε that dictates the interface thickness. These models naturally call for mesh adaptation techniques, which rely on a posteriori error control. However, their error analysis usually deals with the underlying non-monotone nonlinearity via a Gronwall argument which leads to an exponential dependence on ε - 2 . Using an energy argument combined with a topological continuation argument and...

Indefinite integration of oscillatory functions

Paweł Keller (1998)

Applicationes Mathematicae

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A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function ∫ x y i f ( t ) e i ω t d t , -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.

An adaptive finite element method for Fredholm integral equations of the first kind and its verification on experimental data

Nikolay Koshev, Larisa Beilina (2013)

Open Mathematics

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We propose an adaptive finite element method for the solution of a linear Fredholm integral equation of the first kind. We derive a posteriori error estimates in the functional to be minimized and in the regularized solution to this functional, and formulate corresponding adaptive algorithms. To do this we specify nonlinear results obtained earlier for the case of a linear bounded operator. Numerical experiments justify the efficiency of our a posteriori estimates applied both to the...