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On computing Gauss-Kronrod quadrature formulae


Authors: Franca CaliĆ², Walter Gautschi and Elena Marchetti
Journal: Math. Comp. 47 (1986), 639-650, S57
MSC: Primary 65D32
DOI: https://doi.org/10.1090/S0025-5718-1986-0856708-8
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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DOI: https://doi.org/10.1090/S0025-5718-1986-0856708-8
Article copyright: © Copyright 1986 American Mathematical Society

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