Summarizing and completing results by many mathematicians during the past four decades, Fishman, Simmons, and Urbanski provide a complete theory of Diophantine approximation
in the limit set of a group acting on a Gromov hyperbolic metric space.
Keywords: NP completeness, approximation
algorithm, k-median problem
On the basis of existence of parameter manifold, the numeration approximation
systems of iterative levels have been given by backward-forward systems.
The aim of this work is to present an analytical approximation
study of periodic solutions for systems of second-order nonlinear differential equations.
Now we say that the discrete time approximation
[x.sub.h] with the step-size h converges strongly of order y at time T = Nh to the solution X(t) if
They discussed Korovkin-type approximation
properties and rate of convergence of operators (2).
Key words: cosine operator function, Blackman-type approximation
processes, Rogosinski-type approximation
processes, modulus of continuity, Fourier series of symmetric functions with respect to [pi].
The first-order saddlepoint approximation
(FOSA) presented in , is based on the approximation
of the limit state function at the most likelihood point in the original (not standard normal) space.
An efficient initial approximation
was proposed in , although it concentrated on division and square root, it can lead to a solution of inverse square root as well.
A second-order approximation
is obtained by assuming that the change in molar volume with pressure can be described by a constant isothermal compressibility, [[kappa].sub.T] = -1/[v.sub.w][([partial derivative][v.sub.w]/[partial derivative]p).sup.T], which is taken as its value at saturation, [[kappa].sup.sat.sub.T].
The function [[phi].sub.a](x, [epsilon]) is named as asymptotic approximation
of the function [phi](x, [epsilon]).
As an application, for the particular case of CEV model, we obtain an approximation
of the at-the-money (ATM) implied volatility curve as a function of time and an approximation
of the implied volatility smile as a function of the log-moneyness, close to the expiry date.