Sharper error estimates in adaptive quadrature (Q793922)

Consider two quadrature rules A and B which yield approximations \(A_ 1\) and \(B_ 1\) to an unknown integral I. Suppose A is better than B in a certain sense. This is a brief paper where the author points out some difficulties that appear when the quantity \(| A_ 1-B_ 1|\) is used as an estimate of the absolute error \(| I-A_ 1|\). Then he analyzes the error estimates in special cases and gives some examples.