Sharp Error Estimates for Interpolatory Approximation on Convex Polytopes

Sharp Error Estimates for Interpolatory Approximation on Convex Polytopes

Let P be a convex polytope in the d-dimensional Euclidean space. We consider an interpolation of a function f at the vertices of P and compare it with the interpolation of f and its derivative at a fixed point y ∈ P. The two methods may be seen as multivariate analogues of an interpolation by secants and tangents, respectively. For twice continuously differentiable functions, we establish sharp...

Interpolatory Pointwise Estimates for Polynomial Approximation

We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f 2 C 0; 1], by polynomials. For the sake of completeness as well as in order to strengthen some existing results, we discuss brieey the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory es...

Interpolation Error Estimates for Harmonic Coordinates on Polytopes

Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric quality of the triangles in the constrained Delaunay triangulation of the polygon. This characterization is sharp in the sense that families of polyg...

Feasible Region Approximation Using Convex Polytopes

A new technique for polytope approximation of the feasible region for a design is presented. This method is computationally less expensive than the simplicial approximation method [1]. Results on several circuits are presented, and it is shown that the quality of the polytope approximation is substantially better than an ellipsoidal approximation.

Linear time approximation of 3D convex polytopes