# convex combination

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## convex combination

[′kän‚veks ‚käm·bə′nā·shən]
(mathematics)
A linear combination of vectors in which the sum of the coefficients is 1.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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By constructing an appropriate Lyapunov-Krasovskii functional and using the convex combination method and the improved integral inequality, a new less conservative delay-dependent stability criterion is proposed.
Naturally, Minkowski's theorem can be easily extended in the framework of global NPC spaces; that is, each point from a closed convex set can be written as a convex combination of extremal points.
Since [[summation].sup.n.sub.i=1] t[[alpha].sub.i] + [[summation].sup.m.sub.j=1] (1 - t) [[beta].sub.j] = 1, the point tx + (1 - t)y is a convex combination of [u.sub.1], ..., [u.sub.n], [v.sub.1], ..., [v.sub.m], and
Similarly, Pareto efficiency is obtained with any policy p that is a convex combination of [b.sup.A], [b.sup.B], and [b.sup.C].
* It causes no more benchmark of any DMUs to be made from the convex combination of two units in two different times.
According to the terminology in , a Banach space X has the local diameter 2 property if every slice of [B.sub.X] has diameter 2; and X has the strong diameter 2 property if every convex combination of slices of [B.sub.X] has diameter 2, i.e., the diameter of [[summation].sup.n.sub.n=1] [[lambda].sub.i][S.sub.i] is 2, whenever n [member of] N, [[lambda].sub.1], ..., [[lambda].sub.n] [greater than or equal to] 0, with [[summation].sup.n.sub.n=1] [[lambda].sub.i] = 1, and [S.sub.1], ..., [S.sub.n] are slices of [B.sub.X].
Consider the set A' of all d x (d +1) matrices such that each column vector belongs to M and 0 is a convex combination of columns.
In such situations, to allow the use of the Kalman filter, the independence of the sources is often assumed and the correlation is simply ignored in the fusion process, for example, the simple convex combination (SCC) method .
The combined dynamic derivative, also called diamond-[alpha] ([[??].sub.[alpha]]) dynamic derivative ([alpha] [member of] [0,1]), was introduced as a linear convex combination of the well-known delta and nabla dynamic derivatives on time scales.
This means that, in the first case, the evolution operator [V.sub.[alpha]] is a convex combination of two Li-Yorke chaotic operators [V.sub.0], [V.sub.1], meanwhile, in the second case, the evolution operator [W.sub.[alpha]] is a convex combination of the Li-Yorke chaotic and regular operators [W.sub.0], [W.sub.1].

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