The results were compared to those obtained using an EKF and a UKF and showed that the DDF was more accurate than estimators based on a Taylor approximation
like the EKF.
This article establishes that most yield curve models within the popular Nelson and Siegel (1987, hereafter NS) class may be obtained as a formal Taylor approximation
to the dynamic component of the generic Gaussian affine term structure model outlined in Dai and Singleton (2002).
The time delay term is approximated by the Taylor approximation
of the denominator (6) before the controller synthesis.
In section 4 we give an error analysis and the Maple code for the order verification of Taylor approximation
. In section 5 we give a conclusion that briefly summarizes the paper's content.
If q is small enough, the first-order Taylor approximation
can be used, so
Updated capabilities include: wavelength intervals of one, two or five nanometers; support for up to 12 reference scans to eliminate variations in reference measurements; a Taylor approximation
for calculating MPF standard deviations with multiple reference scans and other new features.
If [k.sub.0] is equal to the value of the capital stock in the deterministic steady state and the policy function for labor is smooth, we can use a Taylor approximation
to approximate this policy function around ([k.sub.0], 0, 0) with the form
In particular, it has been established that this approximation is better than the m-fold Taylor expansion--which highlights the fact that for the same amount of matrix-vector products, the Krylov approximation is better than the Taylor approximation
(the Krylov approach involves however more local calculation, notably the Gram-Schmidt sweeps).
The "remainder" term given by the difference between (15) and the first-order Taylor approximation
is controlled by h and will in general deviate from the higher order terms of the Taylor series expansion.
In this paper, we study the relation of the hybrid automaton and its Taylor approximation
in terms of the semantic models, for example, how different similar automata behave, and then the quantitative comparison of the automata.
 have applied Taylor approximation
of order n to the true LLR function such that
for stochastic partial differential equations.