Termination conditions for positivity proving procedures

Authors:
Veronika Pillwein
Affiliations:
Johannes Kepler University, 4040 Linz, Austria
Venue:
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Year:
2013

Citing 12
Cited 0

Partial Cylindrical Algebraic Decomposition for quantifier elimination

Journal of Symbolic Computation
Guarded expressions in practice

ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Solving systems of strict polynomial inequalities

Journal of Symbolic Computation
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition

Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
QEPCAD B: a program for computing with semi-algebraic sets using CADs

ACM SIGSAM Bulletin
A procedure for proving special function inequalities involving a discrete parameter

Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)

Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Computing cylindrical algebraic decomposition via triangular decomposition

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
When can we detect that a P-finite sequence is positive?

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Solving recurrence relations using local invariants

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Effective bounds for P-recursive sequences

Journal of Symbolic Computation
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients

Journal of Symbolic Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Proving positivity of a sequence given by a linear recurrence with polynomial coefficients (P-finite recurrence) is a non-trivial task for both humans and computers. Algorithms dealing with this task are rare or non-existent. One method that was introduced in the last decade by Gerhold and Kauers succeeds on many examples, but termination of this procedure has been proven so far only up to order three for special cases. Here we present an analysis that extends the previously known termination results on recurrences of order three, and also provides termination conditions for recurrences of higher order.