Validated Constraint Compilation

Inaccurate scientific computation is useless at best and dangerous at worst. We address several major sources of inaccuracy. Roundoff error is well known and there is a great deal of work on minimizing it [Act96,Tay97]. By using interval constraints, we don’t eliminate roundoff error, but we make it explicit, so each answer comes with a clear indication of its accuracy. Another source of error arises from misapplying an algorithm (e.g. starting the Newton method with a poor initial choice, or using a method in a case where it does not perform well). We propose a method for reducing the chance of numerical errors in scientific programming by casting the problem as the design of an appropriate constraint solving algorithm and then separating the algorithm design process into two steps.