Some properties of dual quadrature formulae (Q1092260)

A. A. Markov characterized Gaussian quadrature formulas as interpolatory formulas \[ \int f(x)w(x)dx=\Sigma [\nu_ if(x_ i)+\mu_ if'(x_ i)] \] for which the weights \(\mu_ i\) vanish. On the other hand, a formula is called a dual quadrature formula, if \(\nu_ i=0\) for all i. The authors study these formulas by considering formulas for the integrated function \(F(x)=\int^{x}f(t)dt\). The dual formulas can be identified with some formulas which are exact of order 2n-2.