next up previous index
Next: Additional Trouble-shooting Up: How to get the Previous: Interpretation of Parameter Errors   Index

Convergence in MIGRAD, and Positive-definiteness.

MIGRAD uses its current estimate of the covariance matrix of the function to determine the current search direction, since this is the optimal strategy for quadratic functions and ``physical'' functions should be quadratic in the neighbourhood of the minimum at least. The search directions determined by MIGRAD are guaranteed to be downhill only if the covariance matrix is positive-definite, so in case this is not true, it makes a positive-definite approximation by adding an appropriate constant along the diagonal as determined by the eigenvalues of the matrix. Theoretically, the covariance matrix for a ``physical'' function must be positive-definite at the minimum, although it may not be so for all points far away from the minimum, even for a well-determined physical problem. Therefore, if MIGRAD reports that it has found a non-positive-definite covariance matrix, this may be a sign of one or more of the following:


next up previous index
Next: Additional Trouble-shooting Up: How to get the Previous: Interpretation of Parameter Errors   Index
Back to CERN | IT | ASD | CERN Program Library Home
MG (last mod. 1998-08-19)