An Improved One Point Quadrature Formula. (4th December 2021) - Khanna, Nikhil; Arredondo, Juan H.; Kathuria, Leena; Kaushik, S. K.
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 f ∈ L 2 ( R ) in V j, j ∈ Z .