Journal of Inequalities and Applications
Volume 5 (2000), Issue 3, Pages 201-225

On optimal quadrature formulae

Flavia Lanzara

Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, Rome 2 – 00185, Italy

Received 15 April 1999; Revised 4 May 1999

Copyright © 2000 Flavia Lanzara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A procedure to construct quadrature formulae which are exact for solutions of linear differential equations and are optimal in the sense of Sard is discussed. We give necessary and sufficient conditions under which such formulae do exist. Several formulae obtained by applying this method are considered and compared with well known formulae.