Characterizations of Quasiseparable Matrices and Their Subclasses via Recurrence Relations and Signal Flow Graphs
نویسندگان
چکیده
The three-term recurrence relations satisfied by real-orthogonal polynomials (related to irreducible tridiagonal matrices) and the twoand three-term recurrence relations satisfied by the Szegö polynomials (related to unitary Hessenberg matrices) are all well-known. In this paper we consider more general twoand three-term recurrence relations, and prove that the related classes of matrices are all Hessenberg order one quasiseparable ((H, 1)-quasiseparable) matrices. Specifically, we give several characterizations of (H, 1)-quasiseparable matrices and some subclasses including diagonal plus order-one upper semiseparable matrices. Characterizations are given in terms of the quasiseparable generators, in terms of the recurrence relations satisfied by their corresponding systems of polynomials, and in terms of the corresponding signal flow graphs.
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تاریخ انتشار 2007