Verification of numerical programs using Penelope/Ariel

The author describes how asymptotic correctness verifications of numerical programs are performed by using the Penelope Ada verification system. The intuitive notion of closeness underlying the notion of asymptotic correctness and how the notion of asymptotic correctness is supported in Penelope are discussed. A brief description of the Penelope system followed by a discussion of how the Ada real number model is incorporated into it are included. The special mathematical operations introduced for asymptotic correctness are described. The techniques developed for asymptotic correctness proofs are illustrated by an example verification of a program for computing square roots by the Newton iteration method