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]).
The function
approximation problem can be stated formally as follows [5].
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
[34] 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.