SYSTEM REDUCTION VIA TRUNCATED HANKEL-MATRICES

The problem of approximating Hankel operators of finite or infinite rank by lower-rank Hankel operators is considered. For efficiency, truncated Hankel matrices are used as the intermediate step before other existing algorithms such as the CF algorithms are applied to yield the desirable approximants. If the Hankel operator to be approximated is of finite rank, the order of approximation by truncated Hankel operators is obtained. It is also shown that when the mth s-number is simple, then rational symbols of the best rank-m Hankel approximants of the nth truncated Hankel matrices converge uniformly to the corresponding rational symbol of the best rank-m Hankel approximant of the original Hankel operator as n tends to infinity.