Solving Kaltofen's Challenge on Zolotarev's Approximation Problem

Daniel Lazard (1)

1 SPIRAL - Systèmes Polynomiaux, Implantation, Résolution Algébrique

Zolotarev's Approximation problem consists in finding the best approximation of a polynomial of degree n by a polynomial of degree n−2 in the interval [−1, 1]. It is solved for n ≤ 12 by replacing CAD (Cylindrical Algebraic Decomposition) by a strategy consisting in computing first the Zariski closure of the semi-algebraic set which is looked for, before managing the inequalities.

Domaines: Informatique [cs]

Daniel Lazard. Solving Kaltofen's Challenge on Zolotarev's Approximation Problem. The 2006 International Symposium on Symbolic and Algebraic Computation, Jul 2006, Genova, Italy. pp.196-203, ⟨10.1145/1145768.1145803⟩. ⟨hal-01337039⟩