Szegő-Lobatto quadrature rules

Authors:
Carl Jagels;Lothar Reichel
Affiliations:
Department of Mathematics and Computer Science, Hanover College, Hanover, IN 47243, USA;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 10
Cited 5

The QR algorithm for unitary Hessenberg matrices

Journal of Computational and Applied Mathematics
Numerical methods and software

Numerical methods and software
An implementation of a divide and conquer algorithm for the unitary eigen problem

ACM Transactions on Mathematical Software (TOMS)
Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle

Journal of Computational and Applied Mathematics - Special issue on computational complex analysis
On the construction of Szegő polynomials

Journal of Computational and Applied Mathematics - Special issue on computational complex analysis
A connection between quadrature formulas on the unit circle and the interval [ - 1,1]

Journal of Computational and Applied Mathematics
Gaussian quadrature formulae on the unit circle

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
A Stable Divide and Conquer Algorithm for the Unitary Eigenproblem

SIAM Journal on Matrix Analysis and Applications
Positive interpolatory quadrature formulas and para-orthogonal polynomials

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
An Error Analysis of a Unitary Hessenberg QR Algorithm

SIAM Journal on Matrix Analysis and Applications

Trigonometric orthogonal systems and quadrature formulae

Computers & Mathematics with Applications
Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity

Journal of Computational and Applied Mathematics
Orthogonal Laurent polynomials on the unit circle and snake-shaped matrix factorizations

Journal of Approximation Theory
Computation of rational Szegő-Lobatto quadrature formulas

Applied Numerical Mathematics
Positive rational interpolatory quadrature formulas on the unit circle and the interval

Applied Numerical Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

Gauss-type quadrature rules with one or two prescribed nodes are well known and are commonly referred to as Gauss-Radau and Gauss-Lobatto quadrature rules, respectively. Efficient algorithms are available for their computation. Szego quadrature rules are analogs of Gauss quadrature rules for the integration of periodic functions; they integrate exactly trigonometric polynomials of as high degree as possible. Szego quadrature rules have a free parameter, which can be used to prescribe one node. This paper discusses an analog of Gauss-Lobatto rules, i.e., Szego quadrature rules with two prescribed nodes. We refer to these rules as Szego-Lobatto rules. Their properties as well as numerical methods for their computation are discussed.