The \(\sigma\)-orthogonal polynomials: A method of construction. (English) Zbl 0831.65017
Brezinski, Claude (ed.) et al., Orthogonal polynomials and their applications. Proceedings of the third international symposium held in Erice, Italy, June 1-8, 1990. Basel: J. C. Baltzer, IMACS Ann. Comput. Appl. Math. 9, 281-285 (1991).
Summary: Continuing previous work on \(s\)-orthogonal polynomials [cf. G. V. Milovanović, Numerical methods and approximation theory III, 3rd Conf., Nis/Yugosl. 1987 (1988), 311-328 (1988; Zbl 0643.65011)], we develop an iterative method for the construction of \(\sigma\)-orthogonal polynomials with respect to a nonnegative measure on the real line \(\mathbb{R}\). We use a discretized Stieltjes procedure and a version of the secant method for a system of nonlinear equations. Some numerical examples involving Chebyshev and Hermite measures are included.
For the entire collection see [Zbl 0812.00027].
For the entire collection see [Zbl 0812.00027].
MSC:
| 65D20 | Computation of special functions and constants, construction of tables |
| 65D32 | Numerical quadrature and cubature formulas |
| 41A55 | Approximate quadratures |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
