Some Theory Concerning Certification of Mathematical Subroutines by Black Box Testing
Robert P. Roe, John H. Rowland · IEEE Transactions on Software Engineering · 1987
Several inequalities are derived for use in certifying function subroutines by means of black box testing. It is assumed that a function is approximated by means of a polynomial of limited degree on a closed interval. These inequalities give upper bounds on the error of the approximation over the entire interval based on the error measured over a finite sample and known properties of the function.