Is the recurrence relation for orthogonal polynomials always stable?

DOI10.1007/BF01989750zbMath0783.65009MaRDI QIDQ688633

Walter Gautschi

Publication date: 30 November 1993

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialsthree-term recurrence relationpseudostability

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Computation of special functions and constants, construction of tables (65D20)

Related Items (5)

On sensitivity of Gauss-Christoffel quadrature ⋮ On the mathematical nature of Guseinov's rearranged one-range addition theorems for Slater-type functions ⋮ Stable high-order quadrature rules with equidistant points ⋮ Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials ⋮ Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data analysis

Uses Software

• ORTHPOL

Cites Work

• Unnamed Item
• Unnamed Item
• The numerically stable reconstruction of Jacobi matrices from spectral data
• Computing the Hilbert transform of a Jacobi weight function
• Generation and Use of Orthogonal Polynomials for Data-Fitting with a Digital Computer
• Minimal Solutions of Three-Term Recurrence Relations and Orthogonal Polynomials
• On Generating Orthogonal Polynomials
• Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
• Computational Aspects of Three-Term Recurrence Relations
• Numerical solution of second-order linear difference equations

This page was built for publication: Is the recurrence relation for orthogonal polynomials always stable?