Szegö polynomials and quadrature formulas on the unit circle
作者： Leyla Daruis , Pablo González-Vera
DOI: 10.1016/S0168-9274(99)00136-1
关键词: Mathematical analysis 、 Lebesgue measure 、 Unit circle 、 Tanh-sinh quadrature 、 Gauss–Kronrod quadrature formula 、 Numerical integration 、 Quadrature (mathematics) 、 Gauss–Jacobi quadrature 、 Mathematics 、 Clenshaw–Curtis quadrature
摘要: In this paper, computation of the so-called Szego quadrature formulas is considered for some special weight functions on unit circle. The case Lebesgue measure more deeply analyzed. Illustrative numerical examples are also given.
elsevier.com
sci-hub.se 参考文章(15)
Eduardo H. Zarantonello, On trigonometric interpolation Proceedings of the American Mathematical Society. ,vol. 3, pp. 770- 782 ,(1952) , 10.1090/S0002-9939-1952-0050702-4
William B Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle Journal of Computational and Applied Mathematics. ,vol. 46, pp. 183- 198 ,(1993) , 10.1016/0377-0427(93)90294-L
Vladimir Ivanovich Krylov (mathematician), Approximate Calculation of Integrals ,(1962)
Eric G. Wagner, International Series of Numerical Mathematics Mathematics of Computation. ,vol. 17, pp. 210- ,(1963) , 10.2307/2003660
Walter Gautschi, On the construction of Gaussian quadrature rules from modified moments. Mathematics of Computation. ,vol. 24, pp. 245- 260 ,(1970) , 10.1090/S0025-5718-1970-0285117-6
John F. Monahan, Philip J. Davis, Philip Rabinowitz, Methods of Numerical Integration. Journal of the American Statistical Association. ,vol. 80, pp. 1081- ,(1985) , 10.2307/2288607
E. Godoy, F. Marcellan, Orthogonal polynomials and rational modifications of measures Canadian Journal of Mathematics. ,vol. 45, pp. 930- 943 ,(1993) , 10.4153/CJM-1993-052-1
Olav Njåstad, Pablo González-Vera, Erik Hendriksen, Adhemar Bultheel, Orthogonality and quadrature on the unit circle Orthogonal polynomials and their applications. pp. 205- 210 ,(1991)
John B. Conway, Functions of one complex variable ,(1973)
Adhemar Bultheel, Algorithms to Compute the Reflection Coefficients of Digital Filters Numerical Methods of Approximation Theory, Vol. 7 / Numerische Methoden der Approximationstheorie, Band 7. pp. 33- 50 ,(1983) , 10.1007/978-3-0348-6743-6_3