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gauss quadrature error estimation Washington, West Virginia

de Boor CADRE: an algorithm for numerical quadrature J.R. JSTOR, the JSTOR logo, JPASS, and ITHAKA are registered trademarks of ITHAKA. With the n-th polynomial normalized to give Pn(1)= 1, the i-th Gauss node, xi, is the i-th root of Pn; its weight is given by (Abramowitz & Stegun 1972, p.887) w In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain

Check out using a credit card or bank account with PayPal. Appl. Not logged in Not affiliated 130.185.152.138 ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.7/ Connection to 0.0.0.7 failed. J.11, 339–340 (1968)Google Scholar3.Davis, P.J.: Errors of numerical approximation.

Washington D.C., USA; New York, USA: United States Department of Commerce, National Bureau of Standards; Dover Publications. Lyness The effect of inadequate convergence criteria in automatic routines Computer J., 12 (1969), pp. 279–281 [6] J.N. Come back any time and download it again. Think you should have access to this item via your institution?

Lyness When not to use an automatic quadrature routine SIAM Rev., 25 (1983), pp. 63–87 [7] J.N. Mathematics of Computation Vol. 22, No. 101, Jan., 1968 Error Estimates for ... The domain of integration for such a rule is conventionally taken as [−1, 1], so the rule is stated as ∫ − 1 1 f ( x ) d x = Tabulated weights and abscissae with Mathematica source code, high precision (16 and 256 decimal places) Legendre-Gaussian quadrature weights and abscissas, for n=2 through n=64, with Mathematica source code.

doi:10.1090/S0025-5718-1970-0285117-6. Berlin-Heidelberg-New York: Springer 1967Google Scholar9.Stenger, F.: Bounds on the error of Gauss-type quadratures. OpenAthens login Login via your institution Other institution login Other users also viewed these articles Do not show again Skip to main content This service is more advanced with JavaScript available, Taking the limit of x to x i {\displaystyle x_ − 8} yields using L'Hôpital's rule ∏ 1 ≤ j ≤ n j ≠ i ( x i − x j

Your cache administrator is webmaster. The idea underlying the proof is that, because of its sufficiently low degree, h(x) can be divided by p n ( x ) {\displaystyle p_ − 4(x)} to produce a quotient Since scans are not currently available to screen readers, please contact JSTOR User Support for access. Patterson The optimum addition of points to quadrature formulae Math.

the leading coefficient is 1) orthogonal polynomial of degree n and where ( f , g ) = ∫ a b ω ( x ) f ( x ) g ( The trapezoidal rule returns the integral of the orange dashed line, equal to y ( − 1 ) + y ( 1 ) = − 10 {\displaystyle y(-1)+y(1)=-10} . Register or login Buy a PDF of this article Buy a downloadable copy of this article and own it forever. After two weeks, you can pick another three articles.

Berlin; Akademie-Verlag 1967Google Scholar2.Chawla, M.M.: Asymptotic estimates for the error in the Gauss-Legendre quadrature formula. The system returned: (22) Invalid argument The remote host or network may be down. Math. Forgotten username or password?

Patterson On some Gauss and Lobatto based integration formulae Math. Buy article ($34.00) Subscribe to JSTOR Get access to 2,000+ journals. Temme, Nico M. (2010), "§3.5(v): Gauss Quadrature", in Olver, Frank W. Laurie, Dirk P. (1999), "Accurate recovery of recursion coefficients from Gaussian quadrature formulas", J.

Gauss–Kronrod rules are extensions of Gauss quadrature rules generated by adding n + 1 points to an n-point rule in such a way that the resulting rule is of order 2n Miller, ed.), pp. 113–121. Thus ∫ a b ω ( x ) h ( x ) d x = ∫ a b ω ( x ) r ( x ) d x . {\displaystyle \int Help Direct export Save to Mendeley Save to RefWorks Export file Format RIS (for EndNote, ReferenceManager, ProCite) BibTeX Text Content Citation Only Citation and Abstract Export Advanced search Close This document

Lobatto quadrature of function f(x) on interval [−1, 1]: ∫ − 1 1 f ( x ) d x = 2 n ( n − 1 ) [ f ( 1 Think you should have access to this item via your institution? The integral can thus be written as ∫ a b ω ( x ) p n ( x ) x − x i d x = a n a n − Please try the request again.

Kahaner, David; Moler, Cleve; Nash, Stephen (1989), Numerical Methods and Software, Prentice-Hall, ISBN978-0-13-627258-8 Sagar, Robin P. (1991). "A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals". In the 3-term recurrence relation p n + 1 ( x i ) = ( a ) p n ( x i ) + ( b ) p n − 1 Since f ( x j ) = 0 {\displaystyle f(x_{j})=0} for j not equal to i, we have ∫ a b ω ( x ) f ( x ) d x Rational Mech.

London: Academic Press, 1973Google Scholar6.Karlsson, J., von Sydow, B.: The convergence of Padé approximants to series of Stieltjes. Login to your MyJSTOR account × Close Overlay Read Online (Beta) Read Online (Free) relies on page scans, which are not currently available to screen readers. Commun. 66 (2-3): 271–275. In order to preview this item and view access options please enable javascript.

Piessens, E. For example, if the current year is 2008 and a journal has a 5 year moving wall, articles from the year 2002 are available. Ability to save and export citations. Golub, Gene H.; Welsch, John H. (1969), "Calculation of Gauss Quadrature Rules", Mathematics of Computation, 23 (106): 221–230, doi:10.1090/S0025-5718-69-99647-1, JSTOR2004418 Gautschi, Walter (1968). "Construction of Gauss–Christoffel Quadrature Formulas".

Another approach is to use two Gaussian quadrature rules of different orders, and to estimate the error as the difference between the two results. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. Part of Springer Nature. Custom alerts when new content is added.

It is unique up to a constant normalization factor. Items added to your shelf can be removed after 14 days. Phys. Bibcode:2001JCoAM.127..201L.

Please try the request again. MR0331730. Romberg Vereinfachte numerische integration Norske Vid. Login Compare your access options × Close Overlay Purchase Options Purchase a PDF Purchase this article for $34.00 USD.

The method is not, for example, suitable for functions with singularities.