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 ?
5, the constant term of course would result in no vector since there is no directional derivative from au.
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.
0](x,y) denotes the clark generalized directional derivative and [partial derivative]f (x,y) denotes the Clarke subdifferential of f at (x,y).
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.
The one fundamental distinction between the smooth (F-differentiable) and nonsmooth (B-differentiable) functions is the absence of linearity in the directional derivative for nonsmooth functions.
The linear operation G is the directional derivative of J in the direction [phi].
The difference between the smooth (F-differentiable) and non-smooth (Bdifferentiable) functions is the absence of linearity in the directional derivative for non-smooth functions.
exists, is said that F'(x,h) is the directional derivative of F.
F](t) is a conventional forward difference formula for the directional derivative [T.
B](t) is a standard backward difference approximation of the directional derivative.
0](x; v) the Clarke directional derivative of a vector function F [member of] L([R.

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