Editorial: track reliable computations and their applications

Abstract

Many numerical computations, be they solutions to systems of differential equations or optimization problems coming from applied areas like protein folding, do not provide us with guaranteed computation results. In many situations, we have numerical solutions, we may even have a theorem guaranteeing that, eventually, this numerical solution tends to the actual precise one, but the algorithm itself does not provide us with guaranteed bounds on the difference between the numerical approximate solution and the desired actual one. Therefore, in some practical situations, numerical solutions are much farther from the actual (unknown) precise solutions than the users assume.