# compact operator

(redirected from Approximation problem)

## compact operator

[¦käm‚pakt ′äp·ə‚rād·ər]
(mathematics)
A linear transformation from one normed vector space to another, with the property that the image of every bounded set has a compact closure.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In this section, we will apply the Galerkin finite element method [36, 37] to discretize the original problem (TOCP), an infinite-dimensional distributed parameter time optimal control problem, into a semidiscrete approximation problem governed by a finite-dimensional lumped parameter system.
the function approximation problem was chosen as an aim of the experiment.
By (2), we know that the approximation problem of f by polynomials on a domain [OMEGA] is reduced to the well-known approximation problem of its smooth extension F by polynomials on the square T [4, 10].
This method involves approximating the control function by a piecewise-constant function with possible discontinuities at a set of preassigned switching points, which produces an approximation problem such that the solution of this approximation is a suboptimal solution to problem ([OCP.sup.h]).
where [phi](x; [a.sub.0],..., [a.sub.n]) is usually a polynomial [P.sub.n](x) of degree at most n, and the approximation problem can be represented to minimize the error (E):
This problem is so-called the optimal approximation problem with respect to matrix equation (2) (see e.g., [35,8,11-17,24]).
Special topics include simple C*-algebras, approximation properties for groups, the weak expectation property and local lifting property, weakly exact von Neumann algebras, and such applications as Herrero's approximation problem and classification of von Neumann algebras.
The weighted approximation problem is to find a matrix B [element of] [R.sup.m x n] that solves
 investigated a rational approximation problem in connection with the convergence analysis of the ADI iterative method applied to the Stein matrix equation.
Zhang, "Left and right inverse eigenpairs problem of generalized centrosymmetric matrices and its optimal approximation problem," Applied Mathematics and Computation, vol.

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