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Discrete least squares and quadrature formulas


Author: M. Wayne Wilson
Journal: Math. Comp. 24 (1970), 271-282
MSC: Primary 65.55
DOI: https://doi.org/10.1090/S0025-5718-1970-0275677-3
MathSciNet review: 0275677
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Abstract: The purpose of this paper is two-fold. Firstly, we explore some of the intimate connections between discrete least squares processes and quadratures. Secondly, we present an algorithm to construct Gauss-type integration formulas, and consider briefly the method proposed by Gautschi [2].


References [Enhancements On Off] (What's this?)

  • [1] P. J. Davis, Interpolation and Approximation, Blaisdell, Waltham, Mass., 1963. MR 28 #393. MR 0157156 (28:393)
  • [2] W. Gautschi, "Construction of Gauss-Christoffel quadrature formulas," Math. Comp., v. 22, 1968, pp. 251-270. MR 37 #3755. MR 0228171 (37:3755)
  • [3] W. Gautschi, "Algorithm, Gaussian quadrature formulas," Comm. ACM, v. 11, 1968, pp. 432-436.
  • [4] A. H. Stroud & D. Secrest, Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, N.J., 1966. MR 34 #2185. MR 0202312 (34:2185)
  • [5] G. W. Struble, "Orthogonal polynomials: Variable-signed weight functions," Numer. Math. v. 5, 1963, pp. 88-94. MR 27 #4342. MR 0154393 (27:4342)
  • [6] G. Szegö, Orthogonal Polynomials, 2nd ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 21 #5029. MR 0106295 (21:5029)
  • [7] A. E. Taylor, Introduction to Functional Analysis, Wiley, New York, 1958. MR 20 #5411. MR 0098966 (20:5411)
  • [8] V. Tchakaloff, "Formules de cubature méchaniques à coefficients non négatifs," Bull. Sci. Math., (2)v. 81, 1957, pp. 123-134. MR 20 #1145. MR 0094632 (20:1145)
  • [9] M. W. Wilson, Geometrie Aspects of Quadratures with Non-Negative Weights, Ph.D. Thesis, Brown University, Providence, R. I., 1969.
  • [10] M. W. Wilson, "Necessary and sufficient conditions for equidistant quadrature formulas," SIAM J. Numer. Anal. (To appear.) MR 0282530 (43:8241)
  • [11] M. W. Wilson, "A general algorithm for nonnegative quadrature formulas," Math. Comp., v. 23, 1969, pp. 253-258. MR 0242374 (39:3705)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0275677-3
Keywords: Discrete inner product, discrete least squares, least squares approximations, numerical integration, Gaussian integration, orthogonal polynomials, construction of inner products, construction of orthogonal polynomials
Article copyright: © Copyright 1970 American Mathematical Society

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