Optimal cubature formulas in a reflexive Banach space

✍ Scribed by V. L. Vaskevich

• Book ID: 111487623
• Publisher: SP Versita
• Year: 2003
• Tongue: English
• Weight: 185 KB
• Volume: 1
• Category: Article
• ISSN: 1895-1074
• DOI: 10.2478/bf02475665

✦ Synopsis

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.