On the partial realization problem

AbstractIn this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra, most of which were originally developed in other contexts. We approach the partial realization problem from several different angles and explore the connections to such topics as factoriza- tion of Hankel matrices, block tridiagonalization, generalizations of the Lanczos process for biorthogonalization, the Euclidean algorithm and the principal-part con- tinued fractions of Arne Magnus, the Padé table, and the Berlekamp-Masseyalgo- rithm. In this way we are able to clarify some previous results by Rissanen, Kalman, and others and place them in a broader context. This leads to several results and concepts which we think are new. Our analysis is restricted to the scalar case, but some definitions and formulations have been rigged to facilitate an extension to the matrix case