Sentence examples for approximation using the same from inspiring English sources

In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.

The FMT data were reconstructed using the normalised Born approximation using the slab approximation [ 27].

Using the same approximation as in the CDE-PD case, and after some simple algebra, we can find the lower bound of (53) as MSE ̲ 2 CDE − SD = h 1 − ρ 2 + MSE 1 CDE − SD | Δ 2 ≤ MSE 2 CDE − SD. (56).

The well known Tchebyscheff filters can be viewed as a special case of elliptical filters and can be arrived at using the same approximation techniques.

In this first experiment, we study the time performance of TFM-PVALUE compared to LAZYDISTRIBUTION when using the same approximation for the distribution score.

Using the same approximations as for the hysteresis oscillator, the repressilator cycle starts when P3 falls just below K, with P1 at its baseline level β0/ α and P2 roughly equal to (β1/ α) - K. In this regime, (50) P 1 (t ) ≈ (β 0 / α ) e − α t + (β 1 / α ) (1 − e − α t ) P 2 (t ) ≈ − K e − α t + (β 1 / α ) P 3 (t ) ≈ K e − α t + (β 0 / α ) (1 − e − α t ).

The approximation of the critical crack length is performed using the same calibration samples as those used for the approximation of the crack length.

The approximation is depicted in the right side of Fig. 1 using the same parameters as before.

We did, however, make approximations using the FFQ data.

A new theoretical approximation for expectation of the prediction error is derived using the same-realization predictions.

Since convection mostly takes place in the interior of the cell where the temperature is close to the interior temperature T i, we use the same approximation by expanding the exponent E/R T in the Arrhenius form so that the viscosity can be expressed as an exponential function of temperature only: eta = Bexp -gamma T), (3).