partition of unity

(redirected from Partitions of unity)

partition of unity

[pär′tish·ən əv ′yü·nəd·ē]
(mathematics)
On a topological space X, this is a covering by open sets Uαwith continuous functions ƒαfrom X to [0,1], where each ƒαis zero on all but a finite number of the Uα, and the sum of all these ƒαat any point equals 1.
References in periodicals archive ?
Along with the astounding 390 exercises, Treves fully topological vector spaces and spaces of function, with forays into Cauchy filters and Frechet spaces, Hilbert spaces and partitions of unity, then moves to duality and spaces of distribution with radon measures, the continuous linear map and Sobolev spaces, then into tensor products and kernals, which includes very interesting commentary on nuclear mapping.
He concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity.