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Basel; Birkhauser Verlag; 1999, International Series of Numerical Mathematics, p. 159-172, 2013

DOI: 10.1007/978-3-0348-0631-2_9

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Cubature on C^ 1 space

Journal article published in 2012 by Gabriel Turinici ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

We explore in this paper cubature formulas over the space of functions having a rst continuous derivative, i.e., C 1 . We show that the classical Lyons-Victoir formulas are not optimal in this case and explain what is the origin of the loss of optimality and how to construct optimal ones; to illustrate we give cubature formulas up to (including) order 4.