Weight functions admitting repeated positive Kronrod quadrature

Abstract

In this note it is shown that for weight functions of the formw(t)=(1 −t 2)1/2/s m (t), wheres m is a polynomial of degreem which is positive on [−1, +1], successive Kronrod extension of a certain class ofN-point interpolation quadrature formulas, including theN-point Gauss-formula, is always possible and that each Kronrod extension has the positivity and interlacing property.