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Maximal order for quadratures using n evaluations. (English) Zbl 0446.41009


MSC:

41A55 Approximate quadratures
65D32 Numerical quadrature and cubature formulas
41A25 Rate of convergence, degree of approximation
65D30 Numerical integration

Citations:

Zbl 0298.65037
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Full Text: DOI EuDML

References:

[1] Davis, P. J.,Interpolation and approximation. Blaisdell, New York, 1963. · Zbl 0111.06003
[2] Ghizzetti, A. andOssicini, A.,Quadrature formulae. Academic Press, New York, 1970.
[3] International Mathematical andStatistical Libraries, Inc.,The IMSL Library. IMSL, Houston, 1976.
[4] Kung, H. T. andTraub, J. F.,Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Mach.21 (1974), 643–651. · Zbl 0289.65023
[5] Meersman, R.,On maximal order of families of iterations for nonlinear equations. Doctoral Thesis, Vrije Universiteit Brussel, Brussels, 1976. · Zbl 0349.65030
[6] Ralston, A.,A first course in numerical analysis. McGraw-Hill, New York, 1969. · Zbl 0139.31603
[7] Sharma, A.,Some poised and nonpoised problems of interpolation. SIAM Rev.14 (1972), 129–151. · Zbl 0314.65001
[8] Stroud, A. H. andStancu, D. D.,Quadrature formulas with multiple Gaussian nodes. SIAM J. Numer. Anal. (Ser. B)2 (1965), 129–143. · Zbl 0141.13803
[9] Szegö, G.,Orthogonal polynomials. Amer. Math. Soc. Colloquium Publications, Vol. XXIII, Amer. Math. Soc., Providence, R.I., 1959. · Zbl 0089.27501
[10] Traub, J. F.,Iterative methods for the solution of equations. Prentice-Hall, Englewood Cliffs, N.J., 1964. · Zbl 0121.11204
[11] Werschulz, A. G.,Optimal order and minimal complexity of one-step methods for initial-value problems. Report, Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pa., 1976.
[12] Werschulz, A. G.,Maximal order and order of information for numerical quadrature. Mathematics Research Report Number 77-2, University of Maryland, Baltimore County, Baltimore, MD., 1977. To appear in J. Assoc. Comput. Mach. · Zbl 0445.65015
[13] Wozniakowski, H.,Generalized information and maximal order of iteration for operator equations. SIAM J. Numer. Anal.12 (1975), 121–135.
[14] Woźniakowski, H.,Maximal order of multipoint iterations using n evaluations. InAnalytic Computational Complexity, edited by J. F. Traub, Academic Press, New York, 1976, pp. 75–107.
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