Relative/Absolute Error Formulation

With the exception of the Minimax, Gradient Minimax, and Random Minimax optimizers, all other algorithms use two error formulations: relative error and absolute error. (Minimax, Gradient Minimax, and Random Minimax optimizers use only absolute error.)

These error formulations can be expressed using the following equations:

Relative error:

Absolute Error:

where

Isimu and Imeas represent the simulated and target data sets specified in the Inputs page of the optimizer, and

n the number of data points included in each data set.

Special handling is done for the Relative Error case to avoid situations where Imeas(i) is zero or much smaller than the numerator. For the Levenberg-Marquardt optimizer, the formulation is

For the other optimizers, Imeas(i) is used for the denominator for all points except when Imeas(i)==0 and only then is Isimu(i) used in the denominator.

To select the desired error formulation, choose Absolute or Relative from the Error drop-down box on the Extract/Optimize page.

The absolute error is normalized using the RMS of the measured or target data set, which remains a constant quantity during optimization. This normalization assists the optimizer when different inputs are defined, otherwise inputs with a higher order of magnitude would prevail.