Some notes on a method for proving inequalities by computer
arXiv:math/0701020 · doi:10.1007/s00025-015-0485-8
Abstract
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. Using the well-known results of undecidability of the existence of zeros of real elementary functions, we demonstrate that the considered method generally in practice becomes one heuristic for the verification of inequalities. We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm.
in Results in Mathematics 07/2015
References in corpus (5)
- A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions
- Sharpening and generalizations of Shafer-Fink's double inequality for the arc sine function
- Sharpening and generalizations of Shafer's inequality for the arc tangent function
- Concise sharpening and generalizations of Shafer's inequality for the arc sine function
- A concise proof of Oppenheim's double inequality relating to the cosine and sine functions
Cited by in corpus (4)
- A Method of Proving a Class of Inequalities of Mixed Trigonometric Polynomial Functions
- The natural algorithmic approach of mixed trigonometric-polynomial problems
- Accurate approximations of some expressions involving trigonometric functions
- A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions