Minimal solutions of threeterm recurrence relations and orthogonal polynomials
Author:
Walter Gautschi
Journal:
Math. Comp. 36 (1981), 547554
MSC:
Primary 33A65; Secondary 65D20, 65D30
MathSciNet review:
606512
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Abstract: We observe that the wellknown recurrence relation for orthogonal polynomials admits a "minimal solution" if z is outside the spectrum of the mass distribution with respect to which the polynomials are orthogonal and if the moment problem for this distribution is determined. The minimal solution, indeed is , and can be computed accurately by means of the author's continued fraction algorithm. An application is made to special Gausstype quadrature formulas.
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 J. R. Cash, "An extension of Olver's method for the numerical solution of linear recurrence relations," Math. Comp., v. 32, 1978, pp. 497510. MR 0483578 (58:3570)
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 P. Deuflhard, "A summation technique for minimal solutions of linear homogeneous difference equations," Computing, v. 18, 1977, pp. 113. MR 0433927 (55:6897)
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 W. Gautschi, "Questions of numerical condition related to polynomials," in Recent Advances in Numerical Analysis (C. de Boor and G. H. Golub, Eds.), Academic Press, New York, 1978, pp. 4572. MR 519056 (80b:65035)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106065126
PII:
S 00255718(1981)06065126
Keywords:
Minimal solutions of threeterm recurrence relations,
orthogonal polynomials,
moment problem,
modified moments
Article copyright:
© Copyright 1981
American Mathematical Society
