Minimal universal denominators for systems of linear recurrences. Issue 10 (2nd October 2016)

• Record Type: Journal Article
• Authors: Mu, Yan-Ping
• Is Part Of: Journal of difference equations and applications. Volume 22:Issue 10(2016)
• Page Start: 1472
• Page End: 1479
• Publication Date: 2016-10-02
• Subjects: System of linearrecurrences -- universal denominator -- Abramov's bound -- Gosper-Petkovsěk representation; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2016.1202939
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : Abramov's algorithm provides universal denominators for rational solutions to the system of linear recurrences of the form Y ( x + 1 ) = A ( x ) Y ( x ) + G ( x ) . We show that in general Abramov's estimation is optimal. Meanwhile, we show that better estimations can be obtained when A ( x ) is a triangular matrix and when A ( x ) is a constant matrix up to a scalar factor.