Optimal cubature formulas in a reflexive Banach space

• Autorzy: V. Vaskevich
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

optimal cubature formulas; reflexive Banach spaces; best approximation; reproducing mappings; extremal functions of cubature formulas; 65D32; 41A55; 46N05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 1
• Strony: 79-85

Daty

wydano

2003-03-01

online

2003-03-01

Twórcy

autor

V. Vaskevich

• Siberian Division of Russian Academy of Sciences

Bibliografia

• [1] Holmes, R., Geometric Functional Analysis and its Applications. Graduate Texts in Mathematics 24, Springer-Verlag. 1975.
• [2] Sobolev, S.L. and Vaskevich, V.L. The Theory of Cubature Formulas. Kluwer Academic Publishers, Dordrecht, 1997.
• [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.

Identyfikatory

DOI

10.2478/BF02475665