Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXVII, No. 33, pp. 11–41 () 

Quadrature processes – development and new directionsG. V. MilovanovicDepartment Mathematics, Faculty of Electronic Engineering, University of Nis, P. O. Box 73, 18000 Nis, SerbiaAbstract: We present a survey on quadrature processes, beginning with Newton's idea of approximate integration and Gauss' discovery of his famous quadrature method, as well as significant contributions of Jacobi and Christoffel. Beside the stable construction of GaussChristoffel quadratures for classical and nonclassical weights we give some recent applications in the summation of slowly convergent series and momentpreserving spline approximation. Also, we consider quadratures of the maximal degree of precision with multiple nodes, as well as a more general concept of orthogonality with respect to a given linear moment functional and corresponding quadratures of Gaussian type. A short account of nonstandard quadratures of Gaussian type is also included. Finally, we mention the Gaussian integration which is exact on the space of Müntz polynomials. Keywords: Quadrature process; NewtonCotes formula, GaussChristoffel quadrature formula; Orthogonal polynomials; Moments; Moment functional; Threeterm recurrence relation; Weight; Node; Multiple nodes; Summation of series; Momentpreserving spline approximation; Nonstandard quadratures; Müntz polynomials Classification (MSC2000): 41A55, 33C45, 33C47, 42C05, 65D30, 65D32 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 7 Sep 2008. This page was last modified: 20 Jun 2011.
© 2008 Mathematical Institute of the Serbian Academy of Science and Arts
