Sentence examples for errors of equation from inspiring English sources

Numerical results based on the maximum absolute errors of equation (65) are summarized in Table 2 with several choices of N and M. From this table, we see that we can achieve an excellent approximation for the exact solution by using the proposed method for a limited number of the collocation nodes.

are the truncation errors of equations (2.6) and (2.7), respectively.

We estimated the error of Equation 1 at ±1 wt.% by comparison with previous experimental data in terms of Al2O3/SiO2 ratios; the range of arc basalts listed in Table 2 is 0.31 to 0.39.

One is the unmixing residual error of Equation (7) denoted by fRMSE(E), f RMSE ( E ) = RMSE ( E, X ) = 1 N ∑ i = 1 N x i - E α i 2, (7).

Clearly (T(A cap Aneq emptyset) is a necessary condition for the existence of a fixed point of T. The idea of the best proximity point theory is to determine an approximate solution x such that the error of equation (d x,Tx)=0 ) is minimum.

The relative sizes of the three terms contributing to the mean squared error of Equation (1) for the scenarios of Table 1 and [Additional file 1: Supplemental Table S1] are shown in the Supplementary material [Additional file 1].

The correlation coefficients between the error of criterion equation (adoption) and errors of outcome equations (yield equations) in each specification are given in the last row.

Applying the above auxiliary variables definition to (16), the error of equations, δ (i.e., difference of the sides of equations in the noisy channel) which is a zero-mean random variable [6], can be obtained versus auxiliary variables as δ = δ 1 ⋮ δ M ≜ F φ - s = 2 x x i + 2 y y i + ( K i RS S i ) 2 α P - ρ - x i 2 - y i 2 = H v - 1 M v T D v - s (18).

So, we also tried adding an L1 penalty to the error function (7) where E0 is the original error function of Equation 6 and c is a parameter determining the relative import of fitting the data accurately and using "small" weights.

The objective function E(C,I) used is hence a combination of the mean Euclidean distance, i.e. the error measure of Equation 1, and a penalty function.

The ranking error function of Equation 2 has the disadvantage that it does not consider the difference between two scores s i and s j.