Estamos realizando la búsqueda. Por favor, espere...
Abstract: Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and they are fast due to their fourth-order convergence and its asymptotic exactness for an appropriate selection of the variables. For Gauss?Hermite and Gauss?Laguerre quadratures, local Taylor series can be used for computing efficiently the orthogonal polynomials involved, with exact initial values for the Hermite case and first values computed with a continued fraction for the Laguerre case. The resulting algorithms have almost unrestricted validity with respect to the parameters. Full relative precision is reached for the Hermite nodes, without any accuracy loss and for any degree, and a mild accuracy loss occurs for the Hermite and Laguerre weights as well as for the Laguerre nodes. These fast methods are exclusively based on convergent processes, which, together with the high order of convergence of the underlying iterative method, makes them particularly useful for high accuracy computations. We show examples of very high accuracy computations (of up to 1000 digits of accuracy).
Autoría: Gil A., Segura J., Temme N.,
Fuente: Numerische Mathematik
, November 2019, Volume 143, Issue 3, pp 649-682
Editorial: Springer New York LLC
Fecha de publicación: 01/07/2019
Nº de páginas: 33
Tipo de publicación: Artículo de Revista
Proyecto español: MTM2015-67142-P
Url de la publicación: https://link.springer.com/article/10.1007%2Fs00211-019-01066-2
Consultar en UCrea Leer publicación
AMPARO GIL GOMEZ
JOSE JAVIER SEGURA SALA
TEMME, NICO M.