Introduction

The (n-f ra) x (n + m) matrix of the system (1.6) is nonsingular only if the columns of P are linearly independent. Now, for any 7 E lZm, the z-th component of the product P 7 is p(x{) , where p is the polynomial XljLi 7j Pj • Thus the rank of P is ra if and only if p E IIm and p(x_i) = 0, ¿ =1 , 2 , . . . , n, imply p = 0. We assume that m is small enough to give this property for the positions of the interpolation points, which is the polynomial unisolvency condition that has been mentioned.