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Multiple-Precision Correctly Rounded Gauss-Legendre Quadrature

Laurent Fousse 1
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Numerical integration is an operation that is frequently available in multiple precision numerical software packages. The different quadrature schemes used are considered well studied but the roundoff errors that result from the computation are often neglected, and the actual accuracy of the results are therefore seldom rigorously proven. We focus on the Gauss-Legendre quadrature scheme and describe the algorithms needed in our implementation. A thorough error analysis is given as well as experimental error measurements and timings.
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https://hal.inria.fr/inria-00070311
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Submitted on : Friday, May 19, 2006 - 8:00:49 PM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
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  • HAL Id : inria-00070311, version 1

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Laurent Fousse. Multiple-Precision Correctly Rounded Gauss-Legendre Quadrature. [Research Report] RR-5705, INRIA. 2005, pp.17. ⟨inria-00070311⟩

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