Table 1 Observed and calculated frequencies (cm-i) for triatomic molecules Y=X=Y carbon disulfide (CS2) and allene (C3H4) |

Because of the convenient mathematical characteristics of the x -value (it is additive), it is also used to monitor the fit of a model to experimental data in this application the fitted model Y - ABS(/(x,. ..)) replaces the expected probability increment ACP (see Eq. 1.7) and the measured value y, replaces the observed frequency. Comparisons are only carried out between successive iterations of the optimization routine (e.g. a simplex-program), so that critical X -values need not be used. For example, a mixed logarithmic/exponential function Y=Al LOG(A2 + EXP(X - A3)) is to be fitted to the data tabulated below do the proposed sets of coefficients improve the fit The conclusion is that the new coefficients are indeed better. The y-column shows the values actually measured, while the T-columns give the model estimates for the coefficients A1,A2, and A3. The x -columns are calculated as (y- Y) h- Y. The fact that the sums over these terms, 4.783,2.616, and 0.307 decrease for successive approximations means that the coefficient set 6.499... yields a better approximation than either the initial or the first proposed set. If the x sum, e.g., 0.307, [Pg.79]

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