• Ronny Ramlau, Lothar Reichel (Hg.)

ETNA - Electronic Transactions on Numerical Analysis

Bild


Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.

Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at

Bestellung/Order


Bild
ETNA - Electronic Transactions on Numerical Analysis



ISBN 978-3-7001-8258-0
Online Edition



Send or fax to your local bookseller or to:

Verlag der Österreichischen Akademie der Wissenschaften
Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2,
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400
https://verlag.oeaw.ac.at, e-mail: bestellung.verlag@oeaw.ac.at
UID-Nr.: ATU 16251605, FN 71839x Handelsgericht Wien, DVR: 0096385

Bitte senden Sie mir
Please send me
 
Exemplar(e) der genannten Publikation
copy(ies) of the publication overleaf


NAME


ADRESSE / ADDRESS


ORT / CITY


LAND / COUNTRY


ZAHLUNGSMETHODE / METHOD OF PAYMENT
    Visa     Euro / Master     American Express


NUMMER

Ablaufdatum / Expiry date:  

    I will send a cheque           Vorausrechnung / Send me a proforma invoice
 
DATUM, UNTERSCHRIFT / DATE, SIGNATURE

BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
Bild

Computation of Gauss-type quadrature rules

    Carlos F. Borges, Lothar Reichel

ETNA - Electronic Transactions on Numerical Analysis, pp. 121-136, 2024/10/18

doi: 10.1553/etna_vol61s121

doi: 10.1553/etna_vol61s121


PDF
X
BibTEX-Export:

X
EndNote/Zotero-Export:

X
RIS-Export:

X 
Researchgate-Export (COinS)

Permanent QR-Code

doi:10.1553/etna_vol61s121



doi:10.1553/etna_vol61s121

Abstract

Many problems in scientific computing require the evaluation of Gauss quadrature rules. It is important to be able to estimate the quadrature error in these rules. Error estimates or error bounds often can be computed by evaluating an additional related Gauss-type formula such as a Gauss-Radau, Gauss-Lobatto, anti-Gauss, averaged Gauss, or optimal averaged Gauss rule. This paper presents software for both the evaluation of a single Gauss quadrature rule and the calculation of a pair of a Gauss rule and a related Gauss-type rule. The software is based on a divide-and-conquer method. This method is compared to both an available and a new implementation of the Golub-Welsch algorithm, which is the classical approach to evaluate a single Gauss quadrature rule. Timings on a laptop computer show the divide-and-conquer method to be competitive except for the computation of a single quadrature rule with very few nodes.

Keywords: quadrature, Gauss rule, Gauss-Radau rule, Gauss-Lobatto rule, averaged Gauss rule, optimal averaged Gauss rule quadrature, divide-and-conquer method, Golub-Welsch algorithm