UAH > Math > Colloquia > 2/10/2006
In this talk we shall present exact asymptotics of the optimal error of linear spline interpolation of an arbitrary function in various settings, in particular for the case of Lp-norm, 1 ≤ p ≤ ∞, and f in C2([0, 1]2), and for the case of L∞-norm and f in C2([0, 1]d). We shall present review of existing results as well as a series of new ones. Proofs of these results lead to algorithms for construction of asymptotically optimal sequences of triangulations for linear interpolation. Similar results are obtained for near interpolation by bilinear splines.