Short Communication: Weighted dual approach to the problem of equivalent replacement

Abstract

The problem of equivalent replacement plays a basic role in many fields of science and technology. In the classical approach the original object A is to be replaced by an equivalent object kB using the mean square minimum criterion. When the difference between A and kB is significant the replacement leads to unaccepted errors. In order to reduce the errors one may apply the dual approach. One of significant advantages of the dual conception is its consideration of two different aspects of a problem in question allowing the investigation to be more appropriate. The main idea of this short communication is to propose a special form of weighted dual mean square criterion. Numerical results are carried out for linear and nonlinear systems to show an improved accuracy of the proposed criterion.