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 ?
This preconditioner is then applied to the nonlinear operator using a Richardson iteration.
This paper is concerned with the stable computation of a solution of a nonlinear operator equation,
NIETO, Fixed points and approximate solutions for nonlinear operator equations, J.
For a given nonlinear operator T and a point-to-set mapping [K.
K], where I is the identity operator and g is a nonlinear operator.
K], where I is the identity operator and g is a given nonlinear operator such that its inverse exists.
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
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.

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