93-338 Korzh S.A., Ov\^carenko I.E., Ugrinovsky R.A.

Chebyshev's recursion --- some analytical, computational and applied aspects (72K, TeX, plain) Dec 22, 93

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Abstract. We consider polynomials orthogonal with respect to some scalar product on spaces of polynomials on the real line and unit circle. A basic problem in the constructive theory of such polynomials is to determine their three-term recurrence relations. Depending on what is known about the measure corresponding to a given scalar product, there are different ways to proceed. If, as is typical in applications, one knows the measure only through its moment information, the appropriate procedure is an algorithm that goes back to Chebyshev. The algorithm in effect implements the nonlinear map from the given moments or modified moments to the desired recurrence coefficients. We study some algebraic and computational structures connected with scalar products on spaces of polynomials on the real line and unit circle and Chebyshev's algorithm. To illustrate up-to-date versions of the Chebyshev algorithm various applied problems are considered.

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