Formal orthogonal polynomials and Hankel/Toeplitz duality

DOI10.1007/BF02140773zbMath0867.42012MaRDI QIDQ1904148

Adhemar Bultheel, Marc Van Barel

Publication date: 13 July 1997

Published in: Numerical Algorithms (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialsToeplitz matrixHankel matrixSchur complementsEuclidean algorithmthree-term recurrence relationChristoffel-Darboux type formula

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (7)

Algebraic aspects of matrix orthogonality for vector polynomials ⋮ Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations ⋮ Look-ahead methods for block Hankel systems ⋮ Nonlinear functional equations satisfied by orthogonal polynomials ⋮ About families of orthogonal polynomials satisfying Heun's differential equation ⋮ Generalizations of orthogonal polynomials ⋮ Rational approximation in linear systems and control

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Vector orthogonal relations. Vector QD-algorithm
• Padé-type approximation and general orthogonal polynomials
• Algebraic methods for Toeplitz-like matrices and operators
• On the partial realization problem
• I. Schur methods in operator theory and signal processing
• The QR algorithm for unitary Hessenberg matrices
• Displacement ranks of matrices and linear equations
• Division algorithms for continued fractions and the Padé table
• A parallel algorithm for discrete least squares rational approximation
• Matrix interpretations and applications of the continued fraction algorithm
• Formally biorthogonal polynomials and a look-ahead Levinson algorithm for general Toeplitz systems
• A unified approach to various orthogonalities
• Discrete linearized least-squares rational approximation on the unit circle
• Polynômes orthogonaux formels - applications
• Look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems
• Orthonormal polynomial vectors and least squares approximation for a discrete inner product
• Reduction to Tridiagonal Form and Minimal Realizations
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
• Time-variant displacement structure and interpolation problems
• Vector Orthogonal Polynomials and Least Squares Approximation
• A GENERAL SYSTEM OF ORTHOGONAL POLYNOMIALS
• The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis

This page was built for publication: Formal orthogonal polynomials and Hankel/Toeplitz duality