Rectangular Vandermonde matrices on Chebyshev nodes

Abstract We consider a rectangular Vandermonde matrix V on Chebyshev nodes. Using combinatorial identities, we give an explicit factorization of the matrix V , a factorization of thepseudo-inverse of V , and prove that the condition number κ 2 (V) does not depend onthe dimension of nodes set. We also discuss the numerical properties of the proposed formulas.