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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On computing Gauss-Kronrod quadrature formulae


Authors: Franca Caliò, Walter Gautschi and Elena Marchetti
Journal: Math. Comp. 47 (1986), 639-650, S57
MSC: Primary 65D32
MathSciNet review: 856708
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Abstract: We discuss the use of Newton's method for computing Gauss-Kronrod quadrature formulae from modified moments. The underlying nonlinear maps are analyzed from the point of view of numerical condition. A method is indicated of computing the polynomial whose zeros are the Kronrod nodes. Examples include Gauss-Kronrod formulae for integrals with a logarithmic and algebraic singularity at one endpoint. Pertinent numerical results are tabulated in the supplements section at the end of this issue.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1986-0856708-8
PII: S 0025-5718(1986)0856708-8
Article copyright: © Copyright 1986 American Mathematical Society