Manual Number: 00650-014-4
Page A-2
AD12-8 Manual
The QUALITY can be used to indicate how good a particular solution is. If the range of points is
very wide or if the points make transition from negative to positive values, then QUALITY will
suffer. For these cases, it may be better to use multiple polynomials rather than just one. For
example, the following data are taken from the NIST tables for type T thermocouples:
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If we take all the data and compute one 5th order polynomial, the QUALITY is 473.543732; not
very good. Now divide the data into two polynomials; one on the negative side including 0 and one
on the positive side also using 0. The results will show a QUALITY of 90.732620 for the negative
side and a QUALITY of 0.005131 for the positive side. Thus, by using two polynomials, you have
made the positive side very accurate and dramatically improved the negative side.
Accuracy of the negative side can be further improved by adding points. For example, add the
following pairs to the negative side of the polynomial for a type T thermocouple:
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If you run the new data, the QUALITY is improved to 69.555611, but still perhaps not as good as
you would like.
Thus, you may use the QUALITY as a means to determine how good the polynomial is. You can
experiment with both order and number of data points until you are satisfied with the solution.
Incidentally, this example also shows that the smaller the range of x values, the better the solution.
The computational method used is a least squares solution using Gauss Elimination with partial
pivoting to improve accuracy.
