gave a 20/3 factor approximation
algorithm for UkM, which was further improved to 3.25 factor by Charikar and Li in .
According to the approximation
methods in , using backward-forward systems of Swift-Hohenberg equation and u = [P.sub.c]u + [P.sub.s]u = [u.sub.c] + [u.sub.s], we assume the following reduced system:
In the second, we recall most of the preliminary notions and the necessary definitions, and we prove the third approximation
in the general case.
Firstly, consider the Euler-Maruyama approximation
We also discuss weighted approximation
properties of these new operators (3) and (69) and compare with the ones (2) by graphics and the absolute error bound of numerical analysis; we will show that the new ones (3) are better than (2) when approximating to functions f.
The aim of this paper is to introduce an abstract framework of certain approximation
processes using a cosine operator functions concept.
The mean-value first-order saddlepoint approximation
(MVFOSA)  is an alternative to FOSA.
Different from one-piecewise linear approximation
used in , a three-piecewise linear approximation
is presented to compute the initial seed in this paper.
2, we plot contours of the relative error in the first-order approximation
multiplied by [10.sup.6] (i.e., parts per million).
Under these conditions, the approximation
(2) is named as generalized asymptotic expansion.
Note that to apply Ito formula to Black-Scholes function, because the derivatives of this function are not bounded, we have to use an approximation
to the identity and the dominated convergence theorem as it is done, for example, in .
methods can be classified into two categories: the Nystrom method [11,12] and random Fourier features [13,14].