Sentence examples for optimal approximation of the from inspiring English sources

Root mean square error (RMSE): RMSE also measures distortion and is often beneficial to minimize this metric when finding the optimal approximation of the signal.

We prove that the splines yield nearly optimal approximation order while simultaneously its piecewise derivatives provide optimal approximation of the derivatives for smooth functions.

With respect to the maximum norm we characterize the necessary and sufficient condition for the conic section to be optimal approximation of the given planar curve.

Via the attendant global energy scaling, the interface energy model facilitates an atomistic determination of the entire phase field energy as an optimal approximation of the (exact) atomistic energy; no adjustable parameters remain.

The optimal approximation of the classical Theodorsen circulation function will be studied as part of the bridge sectional model building exercise, which can therefore be re-casted in a form suitable for control systems analysis and design.

Percent root difference (PRD): PRD measures distortion in reconstructed biomedical signals, and is defined as: PRD = ∑ n = 1 N ( x ( n ) - x ^ ( n ) ) 2 ∑ n = 1 N x 2 ( n ) × 100%% (33) Root mean square error (RMSE): RMSE also measures distortion and is often beneficial to minimize this metric when finding the optimal approximation of the signal.

where ; then is the optimal approximation of in the view of (B.3).

For computational efficiency, optimization is performed greedily: observations are incrementally added to construct the near-optimal approximation of the optimal design.

There are two natural densities associated with this problem: the discrepancy densityρH, given byρH= liminfr→1−inff⁡∫D 0,r)((1−|z|2)|f z)|−1)2dA(z)1−|z|2∫D(0,r dA z 1−|z|2 which measures the discrepancy in optimal approximation of (1−|z|2)−1 with the modulus of polynomials f, and its relative, the tight discrepancy densityρ⁎H, which will trivially satisfy ρH≤ρ⁎H.

This derivation is enabled by the subspace Karhunen Loève transform which provides the optimal approximation of an original signal in a given subspace, and which has been proposed by the present authors.

The main criterion for the choice of the equivalent circuit is a complete physical design of all its structural elements providing the optimal approximation of experimental impedance hodograph − ImZ = f(ReZ) (Figure 8). Figure 8 The Nyquist diagrams for capacitor systems based on NCM.