Error Formula For Gaussian Quadrature
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Gaussian Quadrature Weights
library or other institution: login Log in to your personal account or through gaussian quadrature 2d your institution. If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies gaussian quadrature python on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader. Mathematics of Computation http://www.ams.org/mcom/1968-22-101/S0025-5718-1968-0223094-5/S0025-5718-1968-0223094-5.pdf Vol. 22, No. 101, Jan., 1968 Error Estimates for ... Error Estimates for Gauss Quadrature Formulas for Analytic Functions M. M. Chawla and M. K. Jain Mathematics of Computation Vol. 22, No. 101 (Jan., 1968), pp. 82-90 Published by: American Mathematical Society DOI: 10.2307/2004765 Stable URL: http://www.jstor.org/stable/2004765 Page Count: 9 Read Online (Free) Download ($34.00) Subscribe ($19.50) Cite this Item Cite https://www.jstor.org/stable/2004765 This Item Copy Citation Export Citation Export to RefWorks Export a RIS file (For EndNote, ProCite, Reference Manager, Zotero…) Export a Text file (For BibTex) Note: Always review your references and make any necessary corrections before using. Pay attention to names, capitalization, and dates. × Close Overlay Journal Info Mathematics of Computation Description: This journal, begun in 1943 as Mathematical Tables and Other Aids to Computation, publishes original articles on all aspects of numerical mathematics, book reviews, mathematical tables, and technical notes. It is devoted to advances in numeri cal analysis, the application of computational methods, high speed calculating, and other aids to computation. Moving Wall Moving Wall: 5 years (What is the moving wall?) Moving Wall The "moving wall" represents the time period between the last issue available in JSTOR and the most recently published issue of a journal. Moving walls are generally represented in years. In rare instances, a publisher has elected to have a "zero" moving wall, so their current issues are available in JSTOR shortly after publication. Note: In calculating the moving wall, the current year is not coun
Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» http://mathworld.wolfram.com/GaussianQuadrature.html 13,594 entries Last updated: Tue Sep 27 2016 Created, developed, and nurturedbyEricWeisstein at WolframResearch Applied Mathematics>Numerical Methods>Numerical Integration> Interactive Entries>Interactive Demonstrations> Gaussian Quadrature Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas at which to evaluate the function . The fundamental theorem of Gaussian gaussian quadrature quadrature states that the optimal abscissas of the -point Gaussian quadrature formulas are precisely the roots of the orthogonal polynomial for the same interval and weighting function. Gaussian quadrature is optimal because it fits all polynomials up to degree exactly. Slightly less optimal fits are obtained from Radau quadrature gaussian quadrature formula and Laguerre-Gauss quadrature. interval are roots of1 To determine the weights corresponding to the Gaussian abscissas , compute a Lagrange interpolating polynomial for by letting (1) (where Chandrasekhar 1967 uses instead of ), so (2) Then fitting a Lagrange interpolating polynomial through the points gives (3) for arbitrary points . We are therefore looking for a set of points and weights such that for a weighting function , (4) (5) with weight (6) The weights are sometimes also called the Christoffel numbers (Chandrasekhar 1967). For orthogonal polynomials with , ..., , (7) (Hildebrand 1956, p.322), where is the coefficient of in , then (8) (9) where (10) Using the relationship (11) (Hildebrand 1956, p.323) gives (12) (Note that Press et al. 1992 omit the factor .) In Gaussian quadrature, the weights are all positive. The error is given by (13) (14) where (Hildebrand 1956, pp.320-321). Other