Univariate amenable functions

Abstract: The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two stable algorithms results in an stable algorithm. In this work, we elaborate in this theory for univariate real analytic functions, providing simple tests for both concepts and producing tables for a number of elementary functions which are or fail to be amenable.