directional derivative


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directional derivative

[də′rek·shən·əl də′riv·əd·iv]
(mathematics)
The rate of change of a function in a given direction; more precisely, if ƒ maps an n-dimensional euclidean space into the real numbers, andx= (x1, …, xn) is a vector in this space, andu= (u1, …, un) is a unit vector in the space (that is, u12+···+ un 2= 1), then the directional derivative of ƒ atxin the direction ofuis the limit as h approaches zero of [ƒ(x+ h u) - ƒ(x)]/ h.
References in periodicals archive ?
A Neumann boundary condition in the Laplace or Poisson equation imposes the constraint that the directional derivative of \phi is some value at some location.
The edges are determined in every direction, as opposed to the operator using the directional derivative of the first order;
In analogy with the directional derivative of a convex function, we introduce the notion of the generalized directional derivative of a locally Lipschitz function f at x [member of] X in the direction h [member of] X by
alpha] and [beta] are constants and [partial derivative]u/[partial derivative]n represents the directional derivative in the direction normal n to the boundary [partial derivative][OMEGA] which by convention points outwards.
In this study, the MSA methods of slope, aspect, first directional derivative gradient operator and combination of altitude and shaded relief were used.
Secondly, the potential's directional derivative in a direction crossing S' and parallel to [?
0](x,y) denotes the clark generalized directional derivative and [partial derivative]f (x,y) denotes the Clarke subdifferential of f at (x,y).
1967; Matheron, 1975; 1986) that the right directional derivative at the origin of the covariogram gA of a convex body equals minus the surface area of the orthogonal projection of the set A.
0](x; v) the Clarke directional derivative of a vector function F [member of] L([R.
exists, is said that F'(x,h) is the directional derivative of F.
If F is a locally Lipschitzian and nonsmooth function and for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] exists, is said that F'(x,h) is the directional derivative of F.
Directional derivative filters were used in order to maximize the detection of straight lines in the original image.

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