Abstract: According to the hierarchical identification principle, a hierarchical gradient based iterative estimation algorithm is derived for multivariable output error moving average systems (i.e., multivariable OEMA-like models) which is different from multivariable CARMA-like models. As there exist unmeasurable noise-free outputs and unknown noise terms in the information vector/matrix of the corresponding identification model, this paper is, by means of the auxiliary model identification idea, to replace the unmeasurable variables in the information vector/matrix with the estimated residuals and the outputs of the auxiliary model. A numerical example is provided. [ABSTRACT FROM AUTHOR]
*ITERATIVE methods (Mathematics), *ALGORITHMS, *LEAST squares, *MATRICES (Mathematics), *MATHEMATICAL symmetry, *NUMERICAL solutions to equations, *FROBENIUS groups, *APPROXIMATION theory
Abstract
Abstract: In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix , a solution can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution to a given matrix in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation. [Copyright &y& Elsevier]