Mathematical aspects of internal magnitude calibration

Abstract

The internal calibration method, introduced by Bunclark and Irwin, is presented as a non-linear optimization process. Two different approaches to solve the problem are presented, the conjugate gradient method, a deterministic optimization algorithm, and simulated annealing, belonging to the class of Monte Carlo methods. Tests with model data show that the conjugate gradient method is superior to simulated annealing in computational effort, if the latter is defined by the number of equivalent functional evaluations. Both methods lead to the same average residual of the objective function. Considering the simplicity of the algorithm, simulated annealing suggests itself for solving optimization problems of high complexity with small theoretical effort.