Bibliography for Gauss-Legendre Quadrature

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  1. Gaussian Quadrature as a Numerical Integration Method for Estimating Area Under the Curve
    Amisaki, T.
    Biological and Pharmaceutical Bulletin, 2001, vol. 24, no. 1, pp. 70-77, Ingenta.  
  2. Stopping functionals for Gaussian quadrature formulas
    Ehrich, S.
    Journal of Computational and Applied Mathematics, 2001, vol. 127, no. ER1-2, pp. 153-171, Ingenta.  
  3. Optimal sensor placement via Gaussian quadrature  
    Miller, Robert E.
    Appl. Math. Comput. 97 (1998), no. 1, 71--97, Math. Sci. Net.  
  4. Generalized Gaussian Quadrature Rules for Systems of Arbitrary Functions  
    J. Ma, V. Rokhlin, S. Wandzura  
    SIAM Journal on Numerical Analysis, Vol. 33, No. 3. (Jun., 1996), pp. 971-996, Jstor.  
  5. Anti-Gaussian Quadrature Formulas  
    Dirk P. Laurie  
    Mathematics of Computation, Vol. 65, No. 214. (Apr., 1996), pp. 739-747, Jstor.  
  6. Comment on: A Gaussian quadrature for the optimal evaluation of integrals involving Lorentzians over a semi-infinite interval.
    Homeier, H.H.H.; Steinborn, E.O.
    Computer physics communications, 1996, vol. 99, no. 1, pp. 77, Ingenta.  
  7. Some error expansions for Gaussian quadrature.
    Hunter, D.B.
    BIT, 1995, vol. 35, no. 1, pp. 64, Ingenta.  
  8. On a Theorem of C. Posse Concerning Gaussian Quadrature of Chebyshev Type  
    Klaus-Jurgen Forster  
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 719-724, Jstor.  
  9. Adaptive Gaussian Integration with the HP48S  
    Lyndell M. Kerley  
    Math. Comput. Ed. 27 (1993), no. 1, 206--214.   
  10. On the Remainder of Gaussian Quadrature Formulas for Bernstein-Szego Weight Functions  
    F. Peherstorfer  
    Mathematics of Computation, Vol. 60, No. 201. (Jan., 1993), pp. 317-325, Jstor.  
  11. Error Bounds for Gaussian and Related Quadrature and Applications to R-Convex Functions  
    Knut Petras  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 2. (Apr., 1992), pp. 578-585, Jstor.  
  12. Exact Gaussian quadrature methods for near-singular integrals in the boundary element method.
    Lutz, Earlin
    Engineering analysis with boundary elements, 1992, vol. 9, no. 3, pp. 233, Ingenta.  
  13. A Note on the Error in Gaussian Quadrature.
    Martin, Clyde
    Applied mathematics and computation, 1992, vol. 47, no. 1, pp. 25, Ingenta.  
  14. Error Estimates in Gaussian Quadrature for Functions of Bounded Variation  
    Klaus-Jurgen Forster, Knut Petras  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 3. (Jun., 1991), pp. 880-889, Jstor.  
  15. On Estimates for the Weights in Gaussian Quadrature in the Ultraspherical Case  
    Klaus-Jurgen Forster, Knut Petras  
    Mathematics of Computation, Vol. 55, No. 191. (Jul., 1990), pp. 243-264, Jstor.  
  16. Gaussian quadrature formulae with fixed nodes
    Johnson, Diane L.
    J. Approx. Theory 53 (1988), no. 3, 239--250, Math. Sci. Net.  
  17. Proof without Words: The Gaussian Quadrature as the Area of Either Trapezoid  
    Mike Akerman  
    Mathematics Magazine: Volume 60, Number 2, (1987), Page: 89.   
  18. The Error Norm of Certain Gaussian Quadrature Formulae  
    G. Akrivis  
    Mathematics of Computation, Vol. 45, No. 172. (Oct., 1985), pp. 513-519, Jstor.  
  19. On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives  
    N. I. Ioakimidis  
    Mathematics of Computation, Vol. 44, No. 169. (Jan., 1985), pp. 191-198, Jstor.  
  20. Composite Hermite-Birkhoff Quadrature Formulas of Gaussian Type  
    Nira Dyn  
    Mathematics of Computation, Vol. 43, No. 168. (Oct., 1984), pp. 535-541, Jstor.  
  21. Rates of Convergence of Gaussian Quadrature for Singular Integrands  
    D. S. Lubinsky, P. Rabinowitz  
    Mathematics of Computation, Vol. 43, No. 167. (Jul., 1984), pp. 219-242, Jstor.  
  22. Error Bounds for Gaussian Quadrature and Weighted-L1 Polynomial Approximation  
    Ronald A. DeVore, L. Ridgway Scott  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 2. (Apr., 1984), pp. 400-412, Jstor.  
  23. Error Bounds for Gaussian Quadrature of Analytic Functions  
    Walter Gautschi, Richard S. Varga  
    SIAM Journal on Numerical Analysis, Vol. 20, No. 6. (Dec., 1983), pp. 1170-1186, Jstor.  
  24. A New Class of Gaussian Quadrature Formulas Based on Birkhoff Type Data  
    Kurt Jetter  
    SIAM Journal on Numerical Analysis, Vol. 19, No. 5. (Oct., 1982), pp. 1081-1089, Jstor.  
  25. Asymptotic Error Estimates for Gaussian Quadrature Formulas  
    T. H. Charles Chen  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 143-152, Jstor.  
  26. Quadratic Integration of Gaussian Processes  
    T. F. Lin  
    Proceedings of the American Mathematical Society, Vol. 81, No. 4. (Apr., 1981), pp. 618-623, Jstor.  
  27. Gaussian Quadrature of Integrands Involving the Error Function  
    J. P. Vigneron, Ph. Lambin  
    Mathematics of Computation, Vol. 35, No. 152. (Oct., 1980), pp. 1299-1307, Jstor.  
  28. On Multiple Node Gaussian Quadrature Formulae  
    David L. Barrow  
    Mathematics of Computation, Vol. 32, No. 142. (Apr., 1978), pp. 431-439, Jstor.  
  29. Some Remarks on the Construction of Extended Gaussian Quadrature Rules  
    Giovanni Monegato  
    Mathematics of Computation, Vol. 32, No. 141. (Jan., 1978), pp. 247-252, Jstor.  
  30. A Note on Extended Gaussian Quadrature Rule  
    Giovanni Monegato  
    Mathematics of Computation, Vol. 30, No. 136. (Oct., 1976), pp. 812-81, Jstor.  
  31. On Generalized Gaussian Quadrature  
    Yudell L. Luke, Bing Yuan Ting, Marilyn J. Kemp  
    Mathematics of Computation, Vol. 29, No. 132. (Oct., 1975), pp. 1083-1093, Jstor.  
  32. Numerical Construction of Gaussian Quadrature Formulas  
    Bernard Danloy
    Mathematics of Computation, Vol. 27, No. 124. (Oct., 1973), pp. 861-869, Jstor.  
  33. Concerning Gaussian-Chebyshev Quadrature Errors  
    Charles K. Chui  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 237-240, Jstor.  
  34. On the Gaussian Integration of Chebyshev Polynomials  
    A. R. Curtis, P. Rabinowitz  
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 207-211, Jstor.  
  35. Trigonometric and Gaussian Quadrature  
    C. J. Knight, A. C. R. Newbery  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 575-581, Jstor.  
  36. On the Construction of Gaussian Quadrature Rules from Modified Moments  
    Walter Gautschi  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 245-260+s1-s52, Jstor.  
  37. Notes on the Tables for Gaussian Quadrature of N. M. Steen, G. D. Byrne and E. M. Gelbard  
    Milton R. Pine  
    Mathematics of Computation, Vol. 23, No. 107. (Jul., 1969), p. 673, Jstor.  
  38. Calculation of Gauss Quadrature Rules
    Gene H. Golub, John H. Welsch
    Mathematics of Computation, Vol. 23, No. 106. (Apr., 1969), pp. 221-230+s1-s10, Math. Sci. Net.  
  39. Error Bounds in Gaussian Integration of Functions of Low-Order Continuity (in Technical Notes and Short Papers)  
    Philip Rabinowitz  
    Mathematics of Computation, Vol. 22, No. 102. (Apr., 1968), pp. 431-434, Jstor.  
  40. Gaussian Integration in the Presence of a Singularity  
    Philip Rabinowitz  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 191-201, Jstor.  
  41. Gaussian Quadrature Formulae (in Technical Notes and Short Papers)  
    Donald G. Anderson  
    Mathematics of Computation, Vol. 19, No. 91. (Jul., 1965), pp. 477-481, Jstor.  
  42. Quadrature Formulas with Multiple Gaussian Nodes  
    A. H. Stroud, D. D. Stancu  
    Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis, Vol. 2, No. 1. (1965), pp. 129-143, Jstor.  
  43. A Gaussian Quadrature Method for the Numerical Solution of the Characteristic Initial Value Problem  (in Technical Notes and Short Papers)  
    J. T. Day  
    Mathematics of Computation, Vol. 17, No. 84. (Oct., 1963), pp. 438-441, Jstor.  
  44. Quadrature Formulas with Simple Gaussian Nodes and Multiple Fixed Nodes  
    D. D. Stancu, A. H. Stroud  
    Mathematics of Computation, Vol. 17, No. 84. (Oct., 1963), pp. 384-394, Jstor.  
  45. The Approximate Solution of an Integral Equation Using High-Order Gaussian Quadrature Formulas (in Technical Notes and Short Papers)  
    Stephen M. Robinson, A. H. Stroud  
    Mathematics of Computation, Vol. 15, No. 75. (Jul., 1961), pp. 286-288, Jstor.  
  46. Gaussian Quadrature with Weight Function xn on the Interval (-1, 1)  
    Harry A. Rothmann  
    Mathematics of Computation, Vol. 15, No. 74. (Apr., 1961), pp. 163-168, Jstor.  
  47. Gaussian Quadrature of Some Integrals Involving Airy Functions  
    J. A. Riley, C. Billings  
    Mathematical Tables and Other Aids to Computation, Vol. 13, No. 66. (Apr., 1959), pp. 97-101, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003