Reconstructing randomly sampled multivariate polynomials from highly noisy data

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade-type approximants from so-called generating polynomials and then ...

Polynomial perturbations of real multivariate measures are discussed and corresponding Christoffel type formulas are found. The 1D Christoffel formula is extended to the multidimensional realm: multivariate orthogonal polynomials are expressed in terms ...

Two doubly indexed families of homogeneous and isobaric polynomials in several indeterminates are considered: the (partial) exponential Bell polynomials B n , k and a new family S n , k Z X 1 , , X n - k + 1 such that X 1 - ( 2 n - 1 ) S n , k and B n , ...