Analysis for Computer Scientists by Michael Oberguggenberger & Alexander Ostermann

Author:Michael Oberguggenberger & Alexander Ostermann
Language: eng
Format: epub, pdf
ISBN: 9783319911557
Publisher: Springer International Publishing

its order is at least 3 (as we already know from the construction). However, additionally

i.e., Simpson’s rule even has order 4.

The best quadrature formulas (high accuracy with little computational effort) are the Gaussian quadrature formulas. For that we state the following result whose proof can be found in [23, Chap. 10, Corollary 10.1].

Proposition 13.7

There is no quadrature formula with s stages of order . On the other hand, for every there exists a (unique) quadrature formula of order . This formula is called s-stage Gaussian quadrature formula.

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