A study of gradient optimization techniques, in particular as applied to system modelling problems, is made. Three efficient techniques are used to derive optimum second-order and third-order models for a seventh-order system. The optimization techniques are the Fletcher-Powell method, a more recent method proposed by Fletcher and a method based on a more general objective function proposed by Jacobson and Oksman.
The approximation is carried out in the time domain. Least squares and least pth criteria are used, and almost minimax results are obtained for large values of p. Values of p up to 10^12 are successfully used. The results are compared with other minimax type algorithms.