Comparison of minimizers, with weighted least squares¶

Here we provide a summary and detailed results for a comparison of minimizers in Mantid when using weights in the cost function. For an explanation of the comparison approach and the results obtained when not using weights see the General comparison of minimizers. In the alternative results presented here the cost function used is least squares and weigths are defined from input observational error estimates. See the general concept page on fitting for an explanation on how the error estimates are used in the least squares cost function. This cost function is named in the list of cost functions available in Mantid as “Least squares”. It is the default cost function in Mantid and the most commonly used for neutron data.

As the NIST problems do not include measurement errors, assuming that these datasets would represent data from a typical Mantid workspace we introduce observational error estimates calculated as the square root of the observations.