@MISC{A_szegő-lobattoquadrature, author = {Carl Jagels A and Lothar Reichel B}, title = {Szegő-Lobatto quadrature rules}, year = {} }

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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. Szegő 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. Szegő 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., Szegő quadrature rules with two prescribed nodes. We refer to these rules as Szegő-Lobatto rules. Their properties as well as numerical methods for their computation are discussed.