Strict Optimal Rational Approximants of Multisequences

The synthesis problem of multisequences of elements of a field
F
is studied. A new way of approximation by rational functions to multisequences is introduced. Different from the usual approach by optimal rational approximant profile, in the proposed strict optimal rational approximant of a multisequence, the components of the optimal rational approximant are not required to have the same denominator. An algorithm to obtain a strict optimal rational approximant profile is established. The relation between optimal rational approximant and strict optimal rational approximant is studied.