Bounds for Linear Recurrences with Restricted Coefficients

Volume 4, Issue 2, 2003

Article 26

BOUNDS FOR LINEAR RECURRENCES WITH RESTRICTED COEFFICIENTS

DEPARTMENT OF MATHEMATICS
WAKE FOREST UNIVERSITY
WINSTON-SALEM, NC 27109.
E-Mail: berenhks@wfu.edu

DEPARTMENT OF STATISTICS
THE UNIVERSITY OF GEORGIA
ATHENS, GA 30602-1952.
E-Mail: lund@stat.uga.edu

Received 16 May, 2002; Accepted 14 February, 2003.
Communicated by: I. Pressman

ABSTRACT. This paper derives inequalities for general linear recurrences. Optimal bounds for solutions to the recurrence are obtained when the coefficients of the recursion lie in intervals that include zero. An important aspect of the derived bounds is that they are easily computable. The results bound solutions of triangular matrix equations and coefficients of ratios of power series.

Key words:
Recurrence, Restricted Coefficients, Power Series, Triangular Matrices.

2000 Mathematics Subject Classification:
39A10, 30B10, 15A45, 15A24, 11B37.

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