Polynomial approximation and quadrature on geographic rectangles

Polynomial approximation and quadrature on geographic rectangles

Using some recent results on subperiodic trigonometric interpolation and quadrature, and the theory of admissible meshes for multivariate polynomial approximation, we study product Gaussian quadrature, hyperinterpolation and interpolation on some regions of Sd, d ≥ 2. Such regions include caps, zones, slices and more generally spherical rectangles defined by longitudes and (co)latitudes (geogra...

Approximation and Quadrature

Let V be a vector space with inner product (u, v) and norm u = (u, u) 1/2. We are given u ∈ V and a subspace˜V = span v (n) are linearly independent. We want to find p ∈ ˜ V such that u − p is minimal.

Localized Linear Polynomial Operators and Quadrature Formulas on the Sphere

The purpose of this paper is to construct universal, auto-adaptive, localized, linear, polynomial (-valued) operators based on scattered data on the (hyper) sphere Sq (q ≥ 2). The approximation and localization properties of our operators are studied theoretically in deterministic as well as probabilistic settings. Numerical experiments are presented to demonstrate their superiority over tradit...

Lectures on multivariate polynomial approximation

Remarks on Piecewise Polynomial Approximation

The theoretical and experimental background for the approximation of "real-world" functions is reviewed to motivate the use of piecewise polynomial approximations. It is possible in practice ~o achieve the results suggested by the theory for piecewise polynomials. A convergent adaptive algorithm is outlined which effectively and efficiently computes smooth piecewise polynomial approxImations to...