Berthold LB 9510, Руководство по эксплуатации

Страница: 76 / 79

9 Appendix LB 9510 Lumat
Page 76 of 79 71450BA2 Rev. 00, 12/2020
This factor is determined according to the formula
the limits 1 <f < 100 are valid for f .
As a consequence, the curve will be fairly linear at the zero point.
Spline Function
The spline
1
. polynomial g
i
(x) is calculated according to the formula:
∫ [
𝒈
"
(
𝒙
)]
𝟐
𝒙
𝒏
𝒙
𝟎
𝒅𝒙 → 𝒎𝒊𝒏
i.e. the waviness of the resulting curve will be minimized, and
∑ [
𝒈
(
𝒙
𝒊
)
− 𝒚
𝒊
𝜹𝒚
𝒊
]
𝟐
𝒏
𝒊=𝟎
≤ 𝑺
i.e. the sum of the squares of the deviations between the calculated
spline curve and the original standard points lei, with regard to the calcu-
lated relative measuring and statistics error
δ yi of all standard points, is
smaller than the smoothing factor S .
The automatic smoothing function ensures that, beginning with smooth-
ing factor 0, the standard curve in the lin-log plot (which is only used for
this!) is checked. It must have either no turning point or just one. If this is
not the case, the spline coefficients are calculated again with a higher
smoothing factor and then the quality of the resulting curve is checked
again. If the maximum smoothing factor is reached and the curve still
1
The Spline polynomial g1(x) is calculated according to the algorithm by REINSCH, Num. Math. 10, 1967, pp. 177-183
N: number of standards
X: standard cocentration