Optimal cubature formulas in a reflexive Banach space |
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Authors: | Vaskevich V. L. |
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Affiliation: | (1) Sobolev Institute of Mathematics, Siberian Division of Russian Academy of Sciences, pr. Koptyuga 4, 630090 Novosibirsk, Russia |
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Abstract: | 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. |
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Keywords: | optimal cubature formulas reflexive Banach spaces best approximation reproducing mappings extremal functions of cubature formulas |
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