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Lobatto quadrature formula

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A quadrature formula of highest algebraic degree of accuracy for the interval and weight with two fixed nodes: the end-points of . The Lobatto quadrature formula has the form

The points are the roots of the polynomial (a Jacobi polynomial), orthogonal on with respect to the weight , and . The algebraic degree of accuracy is . A table of nodes and coefficients of the Lobatto quadrature formula for ( varies from 1 to 15 with step 1) was given in [2] (see also [3]).

The formula was established by R. Lobatto (see [1]).

References

[1] R. Lobatto, "Lessen over de differentiaal- en integraalrekening" , 1–2 , 's Gravenhage (1851–1852)
[2] V.I. Krylov, "Approximate calculation of integrals" , Macmillan (1962) (Translated from Russian)
[3] H.H. Michels, "Abscissas and weight coefficients for Lobatto quadrature" Math. Comp. , 17 (1963) pp. 237–244


Comments

For the notion of algebraic degree of accuracy of a quadrature formula see Quadrature formula.

References

[a1] A.H. Stroud, "Gaussian quadrature formulas" , Prentice-Hall (1966)
How to Cite This Entry:
Lobatto quadrature formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lobatto_quadrature_formula&oldid=33608
This article was adapted from an original article by I.P. Mysovskikh (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article