Economical Models for Functional Covariation - SAMSI

Overview Functional PCA finite element basis Estimation Examples Extensions and discussion
Tent basis functions
φ kl (s, w) satisfies:
φ kl (s, w) is piecewise linear, rather like order 2 splines.
φ kl (s, w) = 1 at vertex (k, l).
φ kl (s, w) = 0 on edges opposite edges of triangles sharing
vertex k, and
All φ kl (s, w) = 0 everywhere else, and basis functions for
edge vertices vanish outside the trapezoidal domain.
As with order 2 splines, basis function (k, l) is a tent
function defined over the hexagon with vertex (k, l) at its
center.
These basis functions are called first order Lagrangian
elements in the numerical literature.