# Optimal cubature formulas in a reflexive Banach space

Open Mathematics (2003)

- Volume: 1, Issue: 1, page 79-85
- ISSN: 2391-5455

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topV. Vaskevich. "Optimal cubature formulas in a reflexive Banach space." Open Mathematics 1.1 (2003): 79-85. <http://eudml.org/doc/268801>.

@article{V2003,

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.},

author = {V. Vaskevich},

journal = {Open Mathematics},

keywords = {65D32; 41A55; 46N05},

language = {eng},

number = {1},

pages = {79-85},

title = {Optimal cubature formulas in a reflexive Banach space},

url = {http://eudml.org/doc/268801},

volume = {1},

year = {2003},

}

TY - JOUR

AU - V. Vaskevich

TI - Optimal cubature formulas in a reflexive Banach space

JO - Open Mathematics

PY - 2003

VL - 1

IS - 1

SP - 79

EP - 85

AB - 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.

LA - eng

KW - 65D32; 41A55; 46N05

UR - http://eudml.org/doc/268801

ER -

## References

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- [2] Sobolev, S.L. and Vaskevich, V.L. The Theory of Cubature Formulas. Kluwer Academic Publishers, Dordrecht, 1997. Zbl0877.65009
- [3] Kutateladze S.S., Fundamentals of Functional Analysis., Kluwer texts in the Math. Sciences: Volume 12, Kluwer Academic Publishers, Dordrecht, 1996, 229 pp.
- [4] Vaskevich, V.L., Best approximation and hierarchical bases. Selçuk Journal of Applied Mathematics. 2001. V. 2, No. 1, P. 83–106. The full text version of the article is available via http://www5.in.tum.de/selcuk/sjam012207.html.
- [5] Bezhaev, A.Yu. and Vasilenko, V.A. Variational Spline Theory. Bull. of Novosibirsk Computing Center. Series: Numerical Analysis. Special Issue: 3. 1993.
- [6] Holmes, R., A Course on Optimization and Best Approximation., Lecture Notes in Math. 257, Springer-Verlag. 1972. Zbl0235.41016