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

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856708-8

MathSciNet review:
856708

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Abstract | References | Similar Articles | Additional Information

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