Using qr-decompositions in the numerical solution of linear recurrence relations

Abstract

For the numerically stable calculation of a solution of a linear recurrence relation the degree of minimality of this solution has to be known. One method to determine the degree of minimality is by calculating the asymptotic behavior of all solutions, a task which is difficult to accomplish for many types of recurrence relations. In this paper we describe a method which uses QR-decomposition for the determination of the degree of minimality

Keywords:

• Recurrence relation
• minimal solution
• QR-decomposition