Finite sequences of orthogonal polynomials connected by a Jacobi matrix

DOI10.1016/0024-3795(86)90180-1zbMath0614.65035OpenAlexW2010428325MaRDI QIDQ1819889

Carl De Boor, Edward B. Saff

Publication date: 1986

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(86)90180-1

zbMATH Keywords

divided differencesJacobi matrixzero setsfinite sequences of orthogonal polynomialsdiscrete least-squares approximation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (16)

Zeros of quasi-orthogonal Jacobi polynomials ⋮ A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials ⋮ The uniqueness of an orthogonality measure ⋮ Construction of acyclic matrices from spectral data ⋮ Persymmetric Jacobi matrices, isospectral deformations and orthogonal polynomials ⋮ Stieltjes interlacing of zeros of little \(q\)-Jacobi and \(q\)-Laguerre polynomials from different sequences ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ Interlacing properties and bounds for zeros of some quasi-orthogonal Laguerre polynomials ⋮ Orthogonal polynomials for self-dual weights ⋮ The theorems of Stieltjes and Favard ⋮ Interlacing of zeros of Gegenbauer polynomials of non-consecutive degree from different sequences ⋮ A \(q\)-generalization of the para-Racah polynomials ⋮ Bounds for zeros of Meixner and Kravchuk polynomials ⋮ Bounds for extreme zeros of some classical orthogonal polynomials ⋮ Limit theorems and soft edge of freezing random matrix models via dual orthogonal polynomials ⋮ Freezing limits for beta-Cauchy ensembles

Cites Work

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• The numerically stable reconstruction of Jacobi matrices from spectral data
• Inverse eigenvalue problems for Jacobi matrices
• Construction of a Jacobi matrix from spectral data
• The numerically stable reconstruction of a Jacobi matrix from spectral data
• On the construction of a Jacobi matrix from spectral data

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