On optimal quadrature formulae (Q1580807)

For integrals involving a nonnegative weight function on a finite interval the author proposes a procedure to construct quadrature formulas which are exact for solutions of linear differential equations and are optimal in the sense of Sard. The author establishes necessary and sufficient conditions for the existence of such formulas. Interesting examples of optimal quadrature formulas, constructed using the proposed method, are given and compared with well-known formulas.