Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | JOHANSSON, Fredrik | |
| hal.structure.identifier | Performance et Qualité des Algorithmes Numériques [PEQUAN] | |
| dc.contributor.author | MEZZAROBBA, Marc | |
| dc.date.accessioned | 2024-04-04T03:05:06Z | |
| dc.date.available | 2024-04-04T03:05:06Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 1064-8275 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193214 | |
| dc.description.abstractEn | We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of realistic parameters, corresponding to the requirements of numerical integration to an accuracy of about 100 to 100 000 bits. Our algorithm combines the summation by rectangular splitting of several types of expansions in terms of hypergeometric series with a fixed-point implementation of Bonnet's three-term recurrence relation. We then compute rigorous enclosures of the Gauss-Legendre nodes and weights using the interval Newton method. We provide rigorous error bounds for all steps of the algorithm. The approach is validated by an implementation in the Arb library, which achieves order-of-magnitude speedups over previous code for computing Gauss-Legendre rules with simultaneous high degree and precision. | |
| dc.description.sponsorship | Approximation rapide et fiable - ANR-14-CE25-0018 | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | Gauss-Legendre quadrature | |
| dc.subject.en | interval arithmetic AMS subject classifications 65Y99 | |
| dc.subject.en | arbitrary-precision arithmetic | |
| dc.subject.en | interval arithmetic | |
| dc.subject.en | Legendre polynomials | |
| dc.subject.en | 65G99 | |
| dc.subject.en | 33C45 | |
| dc.subject.en | Gauss–Legendre quadrature | |
| dc.title.en | Fast and rigorous arbitrary-precision computation of Gauss-Legendre quadrature nodes and weights | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/18M1170133 | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.subject.hal | Informatique [cs]/Logiciel mathématique [cs.MS] | |
| dc.identifier.arxiv | 1802.03948 | |
| bordeaux.journal | SIAM Journal on Scientific Computing | |
| bordeaux.page | C726-C747 | |
| bordeaux.volume | 40 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 6 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01705612 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01705612v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Scientific%20Computing&rft.date=2018&rft.volume=40&rft.issue=6&rft.spage=C726-C747&rft.epage=C726-C747&rft.eissn=1064-8275&rft.issn=1064-8275&rft.au=JOHANSSON,%20Fredrik&MEZZAROBBA,%20Marc&rft.genre=article |
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