Sequences of cubature formulas with a joint countable set of nodes are studied. Each cubature formula under consideration has only a finite number of nonzero weights. We call a sequence of such kind a multicubature formula. For a given reflexive Banach space it is shown that there is a unique optimal multicubature formula and the sequence of the norm of optimal error functionals is monotonically decreasing to 0 as the number of the formula nodes tends to infinity.
@article{bwmeta1.element.doi-10_2478_BF02475665,
author = {V. Vaskevich},
title = {Optimal cubature formulas in a reflexive Banach space},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {79-85},
zbl = {1017.41019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475665}
}
V. Vaskevich. Optimal cubature formulas in a reflexive Banach space. Open Mathematics, Tome 1 (2003) pp. 79-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475665/
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