The theorem of Huet and Lévy stating that for orthogonal rewrite systems (i) everyreducible term contains a needed redex and (ii) repeated contraction of neededredexes results in a normal form if the term under consideration has a normal form,forms the basis of all results on optimal normalizing strategies for orthogonal rewritesystems. However, needed redexes are not computable...

Approximating functions by a linear span of truncated basis sets is standard procedure for the numerical solution differential and integral equations. Commonly used concepts approximation methods are well-posed convergent, provable orders. On down side, however, these often suffer from curse dimensionality, which limits their behavior, especially in situations highly oscillatory target function...