Cubature on C^1 space

Gabriel Turinici ()
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Gabriel Turinici: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

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Abstract: We explore in this paper cubature formulas over the space of functions having a first continuous derivative, i.e., C^1. We show that known cubature 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 9.

Keywords: Cubature Formulae; Stochastic Analysis; Chen Series; cubature on in nite dimensional space; Cubature Wiener (search for similar items in EconPapers)
Date: 2013-06-01
Note: View the original document on HAL open archive server: https://hal.science/hal-00660875v2
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Published in Kristian Bredies, Christian Clason, Karl Kunisch, Gregory Winckel. Control and Optimization with PDE Constraints, Springer Basel, pp.159-172, 2013, International Series of Numerical Mathematics, 978-3-0348-0630-5. ⟨10.1007/978-3-0348-0631-2_9⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00660875

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

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