Residual error

where [E.sup.t.sub.k] is the total average squared residual error. Obviously, the smaller the value of [E.sup.k.sub.k]([c.sup.f.sub.0], [c.sup.s.sub.0], [c.sup.[theta].sub.0], [c.sup.[phi].sub.0]) for given iteration k, the better the approximation.

Wu, "A residual error control scheme in single-hop wireless sensor networks," in Proceedings of the IEEE 27th International Conference on Advanced Information Networking and Applications (AINA '13), pp.

Residual error was within 0.5%, and goodness-of-fit was 24.86 x [10.sup.-6].

Residual error term is classified as overlapping forms (addition forms) and multiplication forms.

Assuming that U([x.sub.r], [t.sub.s]) is the BI-SHAM approximate solution at the collocation (grid) points, the residual error is defined as

where SDit is the standard deviation of the i-th region, ai is the regional fixed effect, gi is the annual growth rate of the i-th region, and eit captures the residual error. Different econometric estimation procedures (fixed, random effect, and stochastic frontier) show that in all cases, portfolio frontier convexity assumption is accepted, as shown by significance, sign, and magnitude of estimated coefficients b1 and b2 values in the period 1980-2010: negative for the first (-0.10) and positive and greater than one for the second (5.37).

Furthermore, we find the residual error of 0.005 is sufficient for the preconditioned DDM-FE-BI-MLFMA while the conventional FE-BI-MLFMA requires a maximum residual error of 0.001 (Fig.

The two sub-matrix equations are solved one by one until the relative residual error is less than a given value.

In Equation 1, [C.cub.i] refers to the test concentration of each response, [AC.cub.50] is the concentration yielding 50% of the maximal response produced by the tested compound (i.e., [EC.cub.50] for activators, [IC.cub.50] for inhibitors), SLOPE determines the shape of the curve and error is the residual error of the model.

Moreover, inversion was done using these solutions as a fixed mechanism with the result indicating a good fit to the data with a final residual error equal to 0.5410 and 0.6040 respectively.

Hence, this paper further employs the exponential series (Hildebrand, 1956) to identify the residual error series resulted from the grey model to further improve the accuracy.