Computation of Gauss-Kronrod quadrature rules with non-positive weights

Electronic Transactions on Numerical Analysis

Volumn 9, Issue , 1999, Pages 26-38

  Ammar, G S ^a   Calvetti, D ^b   Reichel, L ^c  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

^c KENT STATE UNIVERSITY   (United States)

Author keywords

Fast algorithm; Indefinite measure; Inverse eigenvalue problem; Orthogonal polynomials

Indexed keywords

EID: 0003863941     PISSN: 10689613     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. G. Ammar, W. Dayawansa and C. Martin, Exponential interpolation: theory and numerical algorithms, Appl. Math. Comput., 41 (1991), pp. 189-232.
2. A. Bunse-Gerstner, An analysis of the HR-algorithm for computing the eigenvalues of a matrix, Linear Algebra Appl., 35 (1981), pp. 155-173.
3. D. Calvetti, G. H. Golub. W. B. Gragg and L. Reichel, Computation of Gauss-Kronrod quadrature rules, Math. Comp., to appear.
4. J. K. Cullum and R. A. Willoughby, A QL procedure for computing the eigenvalues of complex symmetric tridiagonal matrices, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 83-109.
5. S. Ehrich and G. Mastroianni, Stieltjes polynomials and Lagrange interpolation, Math. Comp., 66 (1997), pp. 311-331.
6. W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Stat. Comput., 3 (1982), pp. 289-317.
7. W. Gautschi, Gauss-Kronrod quadrature - a survey, in Numerical Methods and Approximation Theory III, ed. G. V. Milovanović, University of Niš, 1987, pp. 39-66.
8. W. Gautschi, Orthogonal polynomials and quadrature, Elec. Trans. Numer. Anal., to appear.
9. G. H. Golub and G. Meurant, Matrices, moments and quadrature, in Numerical Analysis 1993, eds. D. F. Griffiths and G. A. Watson, Longman, Essex, England, 1994, pp. 105-156.
10. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, 1996.
11. G. H. Golub and J. H. Welsch, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), pp. 221-230.
12. W. B. Gragg, Matrix interpretations and applications of the continued fraction algorithm, Rocky Mountain J. Math., 4 (1974), pp. 213-225.
13. D. P. Laurie, Calculation of Gauss-Kronrod quadrature rules, Math. Comp., 66 (1997), pp. 1133-1145.
14. F. T. Luk and S. Qiao, Using complex-orthogonal transformations to diagonalize a complex symmetric matrix, in Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, ed. F. T. Luk, Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 3162, The International Society for Optical Engineering, Bellingham, WA, 1997, pp. 418-425.
15. G. Monegato, A note on extended Gaussian quadrature rules, Math. Comp., 30 (1976), pp. 812-817.
16. G. Monegato, Stieltjes polynomials and related quadrature rules, SIAM Rev., 24 (1982), pp. 137-158.
17. L. Reichel, Construction of polynomials that are orthogonal with respect to a discrete bilinear form, Adv. Comput. Math., 1 (1993), pp. 241-258.
18. G. Struble, Orthogonal polynomials: variable-signed weight functions, Numer. Math., 5 (1963), pp. 88-94.
19. G. Szego, Orthogonal Polynomials, 4th ed., Amer. Math. Society, Providence, 1975.
20. D. S. Watkins, Fundamentals of Matrix Computations, Wiley, New York, 1991.