Sentence examples for approximations are needed in from inspiring English sources
Since the yield condition for frame structures is non-linear, piecewise linear approximations are needed in order to apply linear optimization methods.
In addition the Bayesian method provides an exact measure of error for variances and variance ratios, whereas convolute approximations are needed in the classical mixed model method.
Thus, some approximation is needed in practice.
Hence, numerical approximations are needed.
We used quadratic programming because the constraints are needed in approximation.
Elastica are expressed using elliptic integrals (Griffiths 1983; Mumford 1994) for which numerical procedures and approximations (Sharon et al. 2000) are needed in practice.
An appropriate numerical approximation is needed for estimating the underlying functions when dealing with data in the form of discrete sampled points.
Therefore, some form of approximation is needed.
An additional approximation is needed to obtain a computable model.
It may serve as a first step to several problems originating in technical practice where approximation curve parameterizations are needed.
The number of terms in the series in Equation 17 that are needed to get a good approximation is determined by the individual fitness distributions and population size.
