Symbolic-numeric algorithms for computing validated results

In the tutorial, we will introduce two kinds of problems for which validated results are computed via hybrid symbolic-numeric algorithms. These hybrid algorithms follow the basic principle pointed out by Siegfried M. Rump in [1] for computing validated results: First, a pure floating point algorithm is used to compute an approximate solution of good quality for a given problem. Second, a verification step using exact rational arithmetic or interval arithmetic is appended. If this step is successful, then certified lower bounds or verified error bounds are computed for the previously computed approximation.