Gaussian quadrature for sums: A rapidly convergent summation scheme

Mathematics of Computation

Volumn 79, Issue 270, 2010, Pages 857-869

  Monien, H ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77956598293     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-09-02289-3     Document Type: Article

References (26)

1. George A. Baker, Jr., Essentials of Pad́e Approximants, Academic Press, NY, 1975. MR0454459 (56:12710)
2. Carl M. Bender and Steven A. Orzag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978 MR0538168 (80d:00030).
3. Folkmar Bornemann, Dirk Laurie, Stan Wagon, and J̈org Waldvogel, The SIAM 100-digit challenge: A study in high-accuracy numerical computing, SIAM, 2004. MR2076374 (2005c:65002)
4. F. Calogero and A. M. Perelomov, Asymptotic Density of the Zeros of Hermite Polynomials of Diverging Order, and Related Properties of Certain Singular Integral Operators, Lettere al Nuovo Cimento 23 (1978), no. 18, 650-652. MR522774 (80f:33015)
5. F. Calogero, Asymptotic Density of the Zeros of Laguerre and Jacobi Polynomials, Lettere al Nuovo Cimento 23 (1978), no. 18, 653-656. MR522775 (80f:33016)
6. Germund Dahlquist, Summation formulas due to Plana, Lindel̈of and Abel, and related Gauss-Christoffel rules I, BIT 37 (1997), no. 2, 256-295. MR1450961 (99a:65010)
7. Stefan Engblom, Gaussian quadratures with respect to discrete measures, Uppsala University, Technical Report 2006-007 (2006), 1-17.
8. Walter Gautschi, Orthogonal Polynomials, Oxford University Press, 2004. MR2061539 (2005e:42001)
9. Walter Gautschi, The Hardy-Littlewood Function: An Exercise in Slowly Convergent Series, J. Comput. Appl. Math. 179 (2005), 249-254. MR2134369 (2006d:33002)
10. G. H. Golub and J. H. Welsh, Calculation of Gauss quadrature rules, Math. Comp. 23 (1969), 221-230. MR0245201 (39:6513)
11. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, Academic Press, 1994. MR1243179 (94g:00008)
12. Emil Grosswald, Bessel polynomials, Lecture Notes in Mathematics, Springer, 1978. MR520397 (80i:33013)
13. Sven-Ake Gustafson, Convergence acceleration by means of numerical quadrature, BIT 6 (1966), 117-128. MR0205430 (34:5258)
14. Sven-Ake Gustafson, A method of computing limit values, Siam J. Numer. Anal. 10 (1973), no. 6, 1080-1090. MR0343528 (49:8269)
15. D. Levin, Methods for accelerating convergence of infinite series and integrals, Ph.D. thesis, Tel Aviv University, 1975.
16. M. Abramowitz and Irene A. Stegun (ed.), Handbook of Mathematical Functions, Dover, 1965.
17. Gradimir V. Milovanovíc, Various extremal problems of Markov's type for algebraic polynomials, Facta Universitatis (Nis) 2 (1987), 7-28. MR963780 (90c:41010)
18. Gradimir V, Summation of Series and Gaussian Quadratures, Approximation and Computation ISNM 119 (1994), 459-475. MR1333636 (96c:65041)
19. Gradimir V. Milovanovíc and Aleksandar S. Cvetkovíc, An application of little 1/q-Jacobi polynomials to summation of certain series, Facta Univ. Ser. Math. Inform. 18 (2003), 31-46. MR2027228 (2005b:33012)
20. Gradimir V., Convergence of Gaussian Quadrature Rules for Approximation of Certain Sums, Eastern J. on Approximation 10 (2004), 171-187. MR2074906 (2005e:41079)
21. Gradimir V. Milovanovíc, D. S. Mitrivoníc, and Th. M. Rassias, Topics in polynomials: Extremal problems, inequalities, zeros, World Scientific, Singapore, New Jersey, London and Hong Kong, 1994. MR1298187 (95m:30009)
22. Arnold F. Nikiforov and Vasilii B. Uvarov, Special Functions of Mathematical Physics, Birkḧauser Verlag, Basel, 1978. MR0538275 (81b:33001)
23. William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C++, Cambridge University Press, 2002. MR1880993 (2003a:65005)
24. A. Sidi, Practical Extrapolation Methods: Theory and Applications, Cambridge University Press, 2003. MR1994507 (2004e:65005)
25. J. Stoer and R. Burlisch, Introduction to numerical analysis (3rd ed.), Springer, 2002. MR1923481 (2003d:65001)
26. W. Gautschi and Gradimir V. Milovanovíc, Gaussian Quadrature Involving Einstein and Fermi Functions with an Application to Summation of Series, Math. Comp. 44 (1985), no. 169, 177-190. MR771039 (86j:65028)