On the sensitivity of orthogonal polynomials to perturbations in the moments. (English) Zbl 0613.65014
Modification of the moments of a positive weight distribution enables to determine the recursive coefficients of polynomials orthogonal to the given distribution uniquely. The sensitivity of the underlying nonlinear maps with regard to perturbations in the modified moments is analyzed, and pertinent descriptive concepts are introduced. Especially, weight moments of Chebyshev and Jacobi type are discussed.
Reviewer: Y.Kobayashi
MSC:
| 65D20 | Computation of special functions and constants, construction of tables |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
orthogonal polynomial; measure; weak and strong nodes; moments; recursive coefficients; sensitivity; nonlinear maps; perturbations; Chebyshev; JacobiReferences:
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| [3] | Sack, R.A., Donovan, A.F.: An algorithm for Gaussian quadrature given modified moments. Numer. Math.18, 465-478 (1971/72) · Zbl 0221.65041 · doi:10.1007/BF01406683 |
| [4] | Szegö, G.: Orthogonal polynomials. 4th ed., AMS Colloquium Publications23, Providence, R.I.: American Mathematical Society 1975 · Zbl 0305.42011 |
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