Stable high-order cubature formulas for experimental data

In many applications, it is impractical—if not even impossible—to obtain data to fit a known cubature formula (CF). Instead, experimental often acquired at equidistant or scattered locations. this work, stable (in the sense of nonnegative only weights) high-order CFs are developed for purpose. These based on approach allow number points N be larger than basis functions K which integrated exactly by CF. This yields an (N?K)-dimensional affine linear subspace from weights selected that minimize certain norms corresponding stability process, two novel classes proposed and carefully investigated.