Sentence examples for by numerically approximating the from inspiring English sources

A closed form solution for the maximized weights is not known to these authors, so the weights are found by numerically approximating the weights that maximize Equation 14.

In such a case, the diversity order is obtained by numerically approximating the PDF of the equivalent channel for a random variable Δ f uniformly distributed over the interval [-f c, f c ]. Section 5 presents the results from the diversity order with an uniformly distributed CFO.

Approaches for numerically approximating the solution of fractional differential equations have been extensively studied; see, e.g., [38 42].

As the pioneer in numerical methods for such equations, Akrivis et al. [5] numerically approximated the solution of a prototype ultraparabolic equation by applying a fixed-step backward Euler scheme and a second-order box-type finite difference method.

The coefficients and are determined numerically, approximating all the reference wideband codecs in a least-squares sense.

The integration was done numerically by approximating the area under the load-displacement curve by a set of rectangles and summation of the rectangle areas.

The analysis is based on the finding that the Debye scattering function P x) for random flight polymer chains with x = (4πn/λ 2 〈s2〉 sin2 (θ/2) can be numerically approximated by the single term (1 + x/3a)−a with the exponent a near 1.5, where λ/n is the wavelength of incident light in medium and θ is the scattering angle.

By coupling FDM for the lubricating pressure field with FEM for the piston dynamic motion, we numerically approximate the lubricant structure interaction in a reciprocating compressor.

We also use the left rectangular quadrature formula to numerically approximate the integration.

This approach is used here to numerically approximate the conditional densities that enter into the likelihood function of the problem.

To compute Equation (10), we numerically approximate the integral using the rectangle method with the midpoint rule, computing each of the probabilities using the pruning algorithm.