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Displaying similar documents to “Estimation of error in approximate numerical integration near a simple pole using Chebyshev points”

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...

Strong convergence estimates for pseudospectral methods

Wilhelm Heinrichs (1992)

Applications of Mathematics

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Strong convergence estimates for pseudospectral methods applied to ordinary boundary value problems are derived. The results are also used for a convergence analysis of the Schwarz algorithm (a special domain decomposition technique). Different types of nodes (Chebyshev, Legendre nodes) are examined and compared.

Multiple-Precision Correctly rounded Newton-Cotes quadrature

Laurent Fousse (2007)

RAIRO - Theoretical Informatics and Applications

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Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics.
We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds...