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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Starting from primary space, it can be derived other more nuanced representations belonging to multi-valued fuzzy spaces where the set of parameters defines fuzzy partitions of unity. In these multivalued fuzzy spaces, at most four parameters of representation are different from zero while all the others are zero [7], [8], [9], [10].
Now, we introduce an associated partitions of unity [R.sup.n]\{0} that depend on scale j.
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. The book begins with an overview of typical applications of scattered data approximation, then leads the reader from basic properties to the current state of research.