Sigmoidal Transformations and the Trapezoidal Rule
Sigmoidal Transformations and the Trapezoidal Rule
A sigmoidal transformation is a one-to-one mapping of the compact interval [0,1] onto itself whose graph is S-shaped. After giving a formal definition, various mappings already given in the literature are reviewed in the light of the definition. At least one new transformation is introduced and criteria given for generating …