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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Gaussian cubature and bivariate polynomial interpolation
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by Yuan Xu PDF
Math. Comp. 59 (1992), 547-555 Request permission

Abstract:

Gaussian cubature is used to study bivariate polynomial interpolation based on the common zeros of quasi-orthogonal polynomials.
References
  • T. S. Chihara, An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. MR 0481884
  • 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
  • G. Freud, Orthogonal polynomials, Pergamon Press, Oxford, 1971.
  • G. G. Lorentz and R. A. Lorentz, Solvability problems of bivariate interpolation. I, Constr. Approx. 2 (1986), no. 2, 153–169. MR 891966, DOI 10.1007/BF01893422
  • H. Möller, Polynomideale und Kubaturformeln, Thesis, Univ. Dortmund, 1973.
  • H. M. Möller, Kubaturformeln mit minimaler Knotenzahl, Numer. Math. 25 (1975/76), no. 2, 185–200. MR 405815, DOI 10.1007/BF01462272
  • C. R. Morrow and T. N. L. Patterson, Construction of algebraic cubature rules using polynomial ideal theory, SIAM J. Numer. Anal. 15 (1978), no. 5, 953–976. MR 507557, DOI 10.1137/0715062
  • I. P. Mysovskikh, On the construction of cubature formulas with fewest nodes, Soviet Math. 9 (1968), 277-280. —, Numerical characteristics of orthogonal polynomials in two variables, Vestnik Leningrad Univ. Math. 3 (1976), 323-332.
  • I. P. Mysovskikh, The approximation of multiple integrals by using interpolatory cubature formulae, Quantitative approximation (Proc. Internat. Sympos., Bonn, 1979) Academic Press, New York-London, 1980, pp. 217–243. MR 588184
  • Hans Joachim Schmid, On cubature formulae with a minimum number of knots, Numer. Math. 31 (1978/79), no. 3, 281–297. MR 514598, DOI 10.1007/BF01397880
  • Hans Joachim Schmid, Interpolatorische Kubaturformeln, Dissertationes Math. (Rozprawy Mat.) 220 (1983), 122 (German). MR 735919
  • Hans Joachim Schmid, On minimal cubature formulae of even degree, Numerical integration, III (Oberwolfach, 1987) Internat. Schriftenreihe Numer. Math., vol. 85, Birkhäuser, Basel, 1988, pp. 216–225. MR 1021537
  • —, Minimal cubature formulae and matrix equation, preprint.
  • A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0327006
  • Yuan Xu, On the Marcinkiewicz-Zygmund inequality, Progress in approximation theory, Academic Press, Boston, MA, 1991, pp. 879–891. MR 1114822
  • —, On multivariate orthogonal polynomials (submitted).
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 547-555
  • MSC: Primary 65D30; Secondary 41A05
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1140649-8
  • MathSciNet review: 1140649