44
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Empirical mathematics: the first patterson extension of gauss-kronrod rules

, &
Pages 119-129 | Received 14 Mar 1990, Published online: 19 Mar 2007

References

  • Baratella , P. 1979 . Un' estensione ottimale delle formula di quadratura de Radau . Rend. Sem. Mat. Univ. e Politec. Torino , 37 : 147 – 158 .
  • Barrucand , P. 1970 . Inté gration numé rique, abscisse de Kronrod-Patterson et polynomes de Szegö, C. R . Acad. Sci. Paris , 270 : 336 – 338 .
  • Calió , F. , Gautschi , W. and Marchetti , E. 1986 . On computing Gauss-Kronrod quadrature formulae . Math. Comp , 47 : 639 – 650 .
  • Caliò , F. and Marchetti , E. 1987 . Derivation and implementation of an algorithm for singular integrals . Computing , 38 : 235 – 245 .
  • Elhay , S. and Kautsky , J. 1984 . A method for computing quadratures of the Kronrod Patterson type . Austr. Comp. Sci. Comm. , 6 ( No. 1 ) : 15.1 – 15.8 .
  • Elhay S. Kautsky J. Generalized Kronrod Patterson type imbedded quadratures Dept. of Computer Science, Univ. Adelaide 1988 Report TR88-03
  • Gautschi , W. 1988 . “ Gauss-Kronrod quadrature. A survey ” . In Numerical Methods and Approximation Theory III , Edited by: Milovanović , G. V. 39 – 66 . Yugoslavia : Niš .
  • Gautschi , W. and Notaris , S. E. 1988 . An algebraic study of Gauss-Kronrod quadrature formulae for Jacobi weight functions . Math. Comp , 51 : 231 – 248 .
  • Gautschi , W. and Notaris , S. E. 1989 . Gauss-Kronrod quadrature formulae for weight functions of Bernstein-Szegö type . J. Comp. Appl. Math. , 25 : 199 – 224 .
  • Gautschi , W. and Rivlin , T. J. 1989 . A family of Gauss-Kronrod quadrature formulae . Math. Comp. , 51 : 749 – 754 .
  • Kahaner , D. K. and Monegato , G. 1978 . Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights . Z. Angew. Math. Phys. , 29 : 983 – 986 .
  • Kautsky , J. and Elhay , S. 1984 . Gauss quadratures and Jacobi matrices for weight functions not of one sign . Math. Comp. , 43 : 543 – 550 .
  • Kronrod , A. S. 1964 . Integration with control of accuracy . Sov. Phys. Dokl. , 9 : 17 – 19 .
  • Kronrod A. S. Nodes and Weights for Quadrature Formulae Nauko, Moscow 1964 Sixteen-place Tables (Russian) Izelat English translation, Consultants Bureau, New York, 1965
  • Monegato , G. 1976 . A note on extended Gaussian quadrature rules . Math. Comp. , 30 : 812 – 817 .
  • Monegato , G. 1978 . Positivity of the weights of extended Gauss-Legendre quadrature rules . Math. Comp. , 32 : 243 – 245 .
  • Monegato , G. 1979 . “ An overview of results and questions related to Kronrod schemes ” . In Numerische Integration , Edited by: Hammerlin , G. 231 – 240 . Basel : Birkhä user .
  • Monegato , G. 1982 . Stieltjes polynomials and related quadrature rules . SIAM Rev. , 24 : 137 – 158 .
  • Mysovskih I. P. A special case of quadrature formulae containing preassigned nodes (Russian) 1964 4 125 127 Vesci Akad. Navuk. BSSR Ser. Fiz. -Tehn. Navuk
  • Patterson , T. N. L. 1968 . The optimum addition of points to quadrature formulae . Math. Comp , 22 : 847 – 856 .
  • Patterson , T. N. L. 1989 . Algorithm 468: Algorithm for automatic numerical integration over a finite interval . Comm. ACM , 15 : 694 – 699 .
  • Patterson , T. N. L. 123-136 . An algorithm for generating interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions . ACM Trans. Math. Softw. , 15
  • Patterson , T. N. L. 1989 . Algorithm 672: Generation of interpolatory quadrature rules of the highest degree of precision with preassigned nodes for general weight functions . ACM Trans. Math. Softw. , 15 : 137 – 143 .
  • Piessens , R. , de Doneker-Kapenga , E. , Ü berhuber , C. W. and Kahaner , D. K. 1983 . “ Springer Series in Computational Mathematics I ” . In QUADPACK: A Subroutine Package for Automatic Integration , New York : Springer .
  • Rabinowitz , P. 1980 . The exact degree of precision of generalized Gauss-Kronrod integration rules . Math. Comp. , 35 : 1275 – 1283 .
  • Rabinowitz , P. 1983 . Gauss-Kronrod integration rules for Cauchy principal value integrals . Math. Comp. , 41 : 63 – 78 .
  • Rabinowitz , P. 1986 . On the definiteness of Gauss-Kronrod integration rules . Math. Comp. , 46 : 225 – 227 .
  • Szegö , G. 1935 . Ü ber gewisse orthogonale Polynome, die zu einer oszillierenden Belegungsfuntktion gehö ren . Math. Ann. , 110 : 501 – 513 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.