linear map

(redirected from Nonlinear operator)

linear map

(mathematics)
(Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v).
References in periodicals archive ?
such a unified theory could have remarkable consequences even in other fields of mathematics, Including controllability methods in transport theory, A solution of the boundary rigidity problem in geometry, Or a general pseudo-linearization approach for solving nonlinear operator equations.
This nonlinear operator is then used to predict the well logs from the adjacent seismic attributes data (Lindseth, 1979).
The nonlinear operator eigenvalue problem we are concerned with consists of finding a value [lambda] [member of] B([mu], r) := {[lambda] [member of] C : [absolute value of [lambda] - [mu]] < r} close to [mu][member of] C and a nonzero function f such that
where N is a nonlinear operator, x denotes the independent variable, and w(x) is an unknown function.
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the nonlinear operator stemming from the negative p-Laplacian, i.
This nonlinear operator is defined on any 8 bit gray scale 256 x 256 pixel image g (x, y).
Here N(g) is a nonlinear operator from a Hilbert space H into H.
The technique used is based on the decomposition of a solution of nonlinear operator equation in a series of functions.
Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, New York, 2002.
where A, with the appropriate boundary condition (Dirichlet, Neumann, periodic), is a suitable linear, unbounded, self-adjoint and positive operator on a suitable Hilbert space H with dense domain D(A) [subset] H, while F is nonlinear operator and the nonlinear term F(u) can be approximated by Taylor's series (detail is later).

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