An implementation of Christoffel's theorem in the theory of orthogonal polynomials

Author:
David Galant

Journal:
Math. Comp. **25** (1971), 111-113

MSC:
Primary 65.55

MathSciNet review:
0288954

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Abstract: An algorithm for the construction of the polynomials associated with the weight function from those associated with is given for the case when is a polynomial which is nonnegative in the interval of orthogonality. The relation of the algorithm to the *LR* algorithm is also discussed.

**[1]**Gabor Szegö,*Orthogonal polynomials*, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR**0106295****[2]**Eduard L. Stiefel,*Kernel polynomials in linear algebra and their numerical applications*, Nat. Bur. Standards Appl. Math. Ser.**49**(1958), 1–22. MR**0092214****[3]**J. H. Wilkinson,*The algebraic eigenvalue problem*, Clarendon Press, Oxford, 1965. MR**0184422****[4]**Walter Gautschi,*Construction of Gauss-Christoffel quadrature formulas*, Math. Comp.**22**(1968), 251–270. MR**0228171**, 10.1090/S0025-5718-1968-0228171-0**[5]**George E. Forsythe,*Generation and use of orthogonal polynomials for data-fitting with a digital computer*, J. Soc. Indust. Appl. Math.**5**(1957), 74–88. MR**0092208****[6]**Gene H. Golub and John H. Welsch,*Calculation of Gauss quadrature rules*, Math. Comp. 23 (1969), 221-230; addendum, ibid.**23**(1969), no. 106, loose microfiche suppl, A1–A10. MR**0245201**, 10.1090/S0025-5718-69-99647-1

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DOI:
https://doi.org/10.1090/S0025-5718-1971-0288954-8

Keywords:
Numerical construction of orthogonal polynomials,
quotient-difference algorithm,
*LR* algorithm,
Gaussian quadrature,
three-term recurrence relations for orthogonal polynomials

Article copyright:
© Copyright 1971
American Mathematical Society