Abstract
Frequency-dependent material response to an electromagnetic field, complex impedance of electrochemical systems, and effective moduli of composites as functions of the properties of constituent materials can all be expressed in terms of complex analytic functions of Stieltjes class. In fact, any passive, linear, time-invariant system admits such a description. A new definitive algorithm of optimal reconstruction of Stieltjes functions is presented. The main distinguishing feature of the new algorithm is that it presents the certificate of optimality of the underlying least squares problem.