Chebyshev type quadrature formulas
David K. Kahaner
Math. Comp. 24 (1970), 571-574
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Abstract: Quadrature formulas of the form are associated with the name of Chebyshev. Various constraints may be posed on the formula to determine the nodes . Classically the formula is required to integrate th degree polynomials exactly. For and this leads to some complex nodes. In this note we point out a simple way of determining the nodes so that the formula is exact for polynomials of degree less than . For , and we compare our results with others obtained by minimizing the -norm of the deviations of the first monomials from their moments and point out an error in one of these latter calculations.
E. Barnhill, J.
E. Dennis Jr., and G.
M. Nielson, A new type of Chebyshev
quadrature, Math. Comp. 23 (1969), 437–441. MR 0242367
(39 #3698), http://dx.doi.org/10.1090/S0025-5718-1969-0242367-4
Meir and A.
Sharma, A variation of the Tchebicheff quadrature problem,
Illinois J. Math. 11 (1967), 535–546. MR 0216223
K. Kahaner, On equal and almost equal weight quadrature
formulas, SIAM J. Numer. Anal. 6 (1969),
551–556. MR 0286279
B. Hildebrand, Introduction to numerical analysis, McGraw-Hill
Book Company, Inc., New York-Toronto-London, 1956. MR 0075670
- R. Barnhill, J. Dennis & G. Nielson, "A new type of Chebyshev quadrature," Math. Comp., v. 23, 1969, p. 437. MR 0242367 (39:3698)
- A. Meir & A. Sharma, "A variation of the Tchebicheff quadrature problem," Illinois J. Math., v. 11, 1967, pp. 535-546. MR 35 #7058. MR 0216223 (35:7058)
- D. Kahaner, "Equal weight and almost equal weight quadrature formulas," SIAM J. Numer. Anal., v. 6, 1969, pp. 551-556. MR 0286279 (44:3492)
- F. B. Hildebrand, Introduction to Numerical Analysis, McGraw-Hill, New York, 1956, p. 346. MR 17, 788. MR 0075670 (17:788d)
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