An Improved One Point Quadrature Formula. (4th December 2021)

• Record Type: Journal Article
• Authors: Khanna, Nikhil; Arredondo, Juan H.; Kathuria, Leena; Kaushik, S. K.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 2(2021)
• Page Start: 123
• Page End: 131
• Publication Date: 2021-12-04
• Subjects: Wavelets -- scaling function -- MRA -- moments; 42A38 -- 42C40 -- 65T60 -- 44A60; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1870133
• Languages: English
• ISSNs: 0163-0563

Abstract

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 .