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Positive interpolatory cubature formulas (CFs) are constructed for quitegeneral integration domains and weight functions. These CFs are exact forgeneral vector spaces of continuous real-valued functions that containconstants. At the same time, the number of data points -- all of which lieinside the domain of integration -- and cubature weights -- all positive -- isless or equal to the dimension of that vector space. The existence of such CFshas been ensured by Tchakaloff in 1957. Yet, to the best of the author'sknowledge, this work is the first to provide a procedure to successfullyconstruct them.

Constructing Positive Interpolatory Cubature Formulas