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Algebraic methods for modified orthogonal polynomials


Author: David Galant
Journal: Math. Comp. 59 (1992), 541-546
MSC: Primary 42C05; Secondary 65D20
DOI: https://doi.org/10.1090/S0025-5718-1992-1140648-6
MathSciNet review: 1140648
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Abstract: Some algebraic methods are given to implement Uvarov's extended Christoffel theorem. The stability of the algorithms is discussed.


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

  • [1] David Galant, An implementation of Christoffel's theorem in the theory of orthogonal polynomials, Math. Comp. 25 (1971), 111-113. MR 0288954 (44:6149)
  • [2] Walter Gautschi, An algorithmic implementation of the generalized Christoffel theorem, Numerical Integration (G. Hämmerlin, ed.), Internat. Ser. Numer. Math., vol. 57, Birkhäuser, Basel, 1982, pp. 89-106.
  • [3] -, Minimal solutions of three-term recurrence relations and orthogonal polynomials, Math. Comp. 36 (1981), 547-554. MR 606512 (82m:33006)
  • [4] G. H. Golub and J. Kautsky, Calculation of Gauss quadratures with multiple free and fixed knots, Numer. Math. 41 (1983), 147-163. MR 703119 (84i:65030)
  • [5] Peter Henrici, Elements of numerical analysis, Wiley, 1964. MR 0166900 (29:4173)
  • [6] J. Kautsky and G. H. Golub, On the calculation of Jacobi matrices, Linear Algebra Appl. 52/53 (1983), 439-455. MR 709365 (84g:65050)
  • [7] Gabor Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1959. MR 0106295 (21:5029)
  • [8] V. B. Uvarov, On the connection between systems of polynomials orthogonal with respect to different distribution functions, U.S.S.R. Comput. Math. and Math. Phys. 9 (1969), no. 6, 25-36. MR 0262764 (41:7369)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1140648-6
Article copyright: © Copyright 1992 American Mathematical Society

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