Anti-Szego quadrature rules |
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Authors: | Sun-Mi Kim Lothar Reichel |
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Institution: | Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242 ; Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242 |
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Abstract: | Szego quadrature rules are discretization methods for approximating integrals of the form . This paper presents a new class of discretization methods, which we refer to as anti-Szego quadrature rules. Anti-Szego rules can be used to estimate the error in Szego quadrature rules: under suitable conditions, pairs of associated Szego and anti-Szego quadrature rules provide upper and lower bounds for the value of the given integral. The construction of anti-Szego quadrature rules is almost identical to that of Szego quadrature rules in that pairs of associated Szego and anti-Szego rules differ only in the choice of a parameter of unit modulus. Several examples of Szego and anti-Szego quadrature rule pairs are presented. |
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Keywords: | Numerical integration error estimation Szeg\H{o} polynomials trigonometric polynomials |
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