On the sensitivity of orthogonal polynomials to perturbations in the moments
- 1 July 1986
- journal article
- Published by Springer Science and Business Media LLC in Numerische Mathematik
- Vol. 48 (4), 369-382
- https://doi.org/10.1007/bf01389645
Abstract
Modified moments of a positive weight distribution determine uniquely the recursion coefficients of the polynomials orthogonal with respect to the given distribution. We analyze the sensitivity of the underlying nonlinear maps with regard to perturbations in the modified moments and introduce pertinent descriptive concepts. Weight distributions of Chebyshev and Jacobi type are studied in particular.Keywords
This publication has 3 references indexed in Scilit:
- On Generating Orthogonal PolynomialsSIAM Journal on Scientific and Statistical Computing, 1982
- An algorithm for Gaussian quadrature given modified momentsNumerische Mathematik, 1971
- Orthogonal Polynomials. By G. Szegö. Pp. ix, 401. $6. 1939. American Mathematical Society Colloquium Publications, 23. (American Mathematical Society, New York)The Mathematical Gazette, 1940