Some notes on a method for proving inequalities by computer

摘要

In this article we consider mathematical fundamentals of one method forproving inequalities by computer, based on the Remez algorithm. Using thewell-known results of undecidability of the existence of zeros of realelementary functions, we demonstrate that the considered method generally inpractice becomes one heuristic for the verification of inequalities. We givesome improvements of the inequalities considered in the theorems for which theexisting proofs have been based on the numerical verifications of Remezalgorithm.