Cubature formulas on combinatorial graphs

Details Cubature formulas on combinatorial graphs Cubature formulas on combinatorial graphs

2011-04-05

arxiv.org/abs/1104.0963v2

Mathematics

Functional Analysis

Submitted

Scientific paper

The goal of the paper is to establish cubature formulas on finite combinatorial graphs. Two types of cubature formulas are developed. Cuba- ture formulas of the first type are exact on spaces of variational splines on graphs. Since badlimited functions can be obtained as limits of variational splines we obtain cubature formulas which are "essentially" exact on spaces of bandlimited functions. Cubature formulas of the second type are exact on spaces of bandlimited functions. Accuracy of a cubature formulas is given in terms of smoothness of functions. The results have potential applications to problems that arise in data mining.

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