Quintic polynomial

And the nine-point S-G second derivative with a Quartic or Quintic polynomial fit has the coefficients ... 

The first quartile of a sequence of numbers is the number such that one quuarter of the numbers in the sequence are less than this number, quintic polynomial... 

Fig. 2. Calculated O-M-O bending potential energy curves for H2M(OH)2 (M = Si, Ge, Sn). A quintic polynomial, Fo-m-o(0, was fitted to the calculated data (Eq. 2).

The parabola (second degree polynomial) can only be fitted over a limited range (Fig. 15.11). For case a, the parabola is fitted between the log dilutions of 3 and 4.5 (regression formula in Fig. 15.11), whereas in case b the regression curve is fitted between the log dilutions of 1 and 5 (regression formula A = 0.6754 — 0.4417 (log D) -t- 0.0599 (log oy). Cubic, quartic, or quintic polynomials were calculated by the methods discussed in great detail by Snedecor and Cochran (1967). 

The highest order of the integrated smoothing polynomial is not always the best result. In Fig. 4-20, it is shown that the quadratic-cubic polynomial generates less noise than the quartic-quintic polynomial. 

The fitting by higher polynomials (cubic, quartic, quintic) is closer (Table 15.2), however, outlying observations tend to bend the curve and calculation without automation is time-consuming. 

Figure 4-20. Influence of smoothing polynomial order on noise. Second derivative of NiCl2 6 H2O (40 g in water) MD D (S-G). a) 25 points, quadratic-cubic b) 25 points, quartic-quintic c) 15 points, quadratic-cubic d) 15 points, quartic-quintic [14, 15].

Different functional dependences may be used for gradient-index AR layers. The simplest one is linear, but various polynomial dependences are met, for instance cubic or quintic. Sinusoidal dependence is also used. Of these, quintic dependence has been reported as the closest to optimum [164]. 

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