On the definiteness of Gauss-Kronrod integration rules
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- by Philip Rabinowitz PDF
- Math. Comp. 46 (1986), 225-227 Request permission
Abstract:
The nondefiniteness of the Kronrod extension of the Gauss-Gegenbauer integration rule with weight function $w(x;\mu ) = {(1 - {x^2})^{\mu - 1/2}}$, $0 < \mu < 1$, is shown when there are more than three abscissas.References
- G. Akrivis and K.-J. Förster, On the definiteness of quadrature formulae of Clenshaw-Curtis type, Computing 33 (1984), no. 3-4, 363–366. MR 773935, DOI 10.1007/BF02242279
- Philip J. Davis and Philip Rabinowitz, Methods of numerical integration, 2nd ed., Computer Science and Applied Mathematics, Academic Press, Inc., Orlando, FL, 1984. MR 760629
- Philip Rabinowitz, The exact degree of precision of generalized Gauss-Kronrod integration rules, Math. Comp. 35 (1980), no. 152, 1275–1283. MR 583504, DOI 10.1090/S0025-5718-1980-0583504-6
Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Math. Comp. 46 (1986), 225-227
- MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1986-0815844-2
- MathSciNet review: 815844