For any set N [subset] [0,1] of d distinct collocation nodes, we define the polynomial space

The following result characterizes the polynomial space [Q.

Problems in EXP, NEXP, or EXPSPACE are expected or known to not have polynomial space algorithms, an apparently more stringent condition than not having polynomial time algorithms.

21, we show that the complexity of policy existence problems makes a jump from polynomial time to polynomial space if we consider compressed MDPs instead of flat MDPs.

In the framework of polynomial interpolation, Fekete points are points that maximize the Vandermonde determinant (in any polynomial basis) on a given compact set and thus ensure that the corresponding Lebesgue constant grows (at most) algebraically, being bounded by the dimension of the polynomial space.

j]) is a basis of the total-degree polynomial space,

We shall show, that the

polynomial space composed of simple polynomials is not a Haar space.

Observe that this constructive approach immediately yields unisolvence of the interpolation problem, since for any given basis of the underlying polynomial space [V.

First, it comes easy to bound the Lebesgue constant linearly in the dimension of the polynomial space V, which already shows that the Xu points are good candidates for interpolation purposes.

8] Carl de Boor, Nira Dyn, and Amos Ron, On two

polynomial spaces associated with a box spline, Pacific J.

d+1], making use of elementary maps between the three domains and symmetry of the polynomial spaces on these domains.

5) between the three domains and the relations between polynomial spaces as given in Lemma 2.