Sampling and cubature on sparse grids based on a B-spline quasi-interpolation

Dinh Dũng

Let $X_n=\{x^j{\}}_{j=1}^n$ be a set of $n$ points in the $d$-cube $[0,1{]}^d$, and ${\Phi }_n=\{{\phi }_j{\}}_{j=1}^n$ a family of $n$ functions on $[0,1{]}^d$. We consider the approximate recov…