Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants

Françoise Foucher (1) , Paul Sablonnière (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IRMAR - Institut de Recherche Mathématique de Rennes

Given a bivariate function $f$ defined in a rectangular domain $\omega$, we approximate it by a $C^1$ quadratic spline quasi-interpolant (abbr. QI) and we take partial derivatives of this QI as approximations to those of $f$. We give error estimates and asymptotic expansions for these approximations. We also propose a simple algorithm for the determination of stationary points, illustrated by a numerical example.

Mots clés: partial derivative approximation; quadratic spline quasi-interpolant; stationary points detection

Domaines: Analyse numérique [math.NA]

Françoise Foucher, Paul Sablonnière. Approximating partial derivatives of first and second order by quadratic spline quasi-interpolants. Mathematics and Computers in Simulation, 2008, 77 (2-3), pp.202--208. ⟨10.1016/j.matcom.2007.08.021⟩. ⟨hal-00071295⟩