The tolerance used by Brent minimization is controlled by the BrentTolerance option. In the previous section we displayed a fit of synthetic data by Pearson and York to a straight line. Here we shall repeat the fit but turn off significant figure adjustment of the result using the UseSignificantFigures option that is discussed in a later section of this document.
We will then repeat the fit decreasing the tolerance from its default value of .001 to 0.000001 by typing the new value in the appropriate field of the Fit Option setup screen:
For the data, the exact solutions to the fit are known. The table summarises the two fits to the data and compares to the exact solutions:
| BrentTolerance = default | BrentTolerance = 0.000001 | Exact Solutions |
|---|---|---|
| A0 = 5.48072 ±
0.281926 A1 = -0.480678 ± 0.0575653 Chi Squared = 11.8237 |
A0 = 5.48016 ±
0.281355 A1 = -0.480563 ± 0.0574385 Chi Squared = 11.8237 |
A0 = 5.47991025 A1 = -.480533415 |
Decreasing the tolerance gives an answer that is a bit closer to the exact values. Considering the size of the calculated errors in the fit parameters, these two results are essentially the same.
This help document is Copyright © 1999 David M. Harrison. The sample screens are Copyright © 1999 Solomon R.C. Douglas and David M. Harrison. This is version 1.1 of the help document, date (m/d/y) 11/25/99.