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An Improved One Point Quadrature Formula

Abstract Sweldens and Piessens [23] gave the crucial relationship between the first and the second scaling moment in order to derive an effective one-point quadrature formula to reproduce polynomials up to degree 2. Finěk [6] derived quadrature formulas with exactness for polynomials of degree 3 with the use of scaling functions of the Daubechies wavelets. In this paper, some relations between the moments of the scaling function associated with multiresolution analysis are derived and a one point quadrature formula with degree of precision 4 is constructed which helps in the approximation of a function in