Bibliography for Gauss-Legendre Quadrature

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  1. Gaussian quadrature formulae on the unit circle
    Daruis, L.; Gonzalez-Vera, P.; Marcellan, F.
    Journal of Computational and Applied Mathematics, 2002, vol. 140, no. ER1-2, pp. 159-183, Ingenta.  
  2. On the weights of nearly Gaussian quadrature formulae  
    Nikolov, Geno  
    East J. Approx. 7 (2001), no. 1, 115--120, Math. Sci. Net.  
  3. Error bounds for Simpson's quadrature through zero mean Gaussian with covariance
    Hong, B. I.; Choi, S. H.; Hahm, N.
    Communications- Korean Mathematical Society, 2001, vol. 16, no. 4, pp. 691-701, Ingenta.  
  4. Addendum to: Why Gaussian quadrature in the complex plane?
    Saylor, P. E.; Smolarski, D. C.
    Numerical Algorithms, 2001, vol. 27, no. 2, pp. 215-217, Ingenta.  
  5. Generalized Gaussian quadrature applied to an inverse problem in antenna theory
    de Villiers, G. D.; Marchaud, F. B. T.; Pike, E. R.
    Inverse Problems, 2001, vol. 17, no. 4, pp. 1163-1180, Ingenta.  
  6. Gaussian quadrature rules with simple node-weight relations
    De Andrade, E. X. L.; Bracciali, C. F.; Ranga, A. S.
    Numerical Algorithms, 2001, vol. 27, no. 1, pp. 61-76, Ingenta.  
  7. Boundary solution of Poisson's equation using radial basis function collocated on Gaussian quadrature nodes
    Elansari, M.; Ouazar, D.; Cheng, A. H.-D.
    Communications in Numerical Methods in Engineering, 2001, vol. 17, no. 7, pp. 455-464, Ingenta.  
  8. Why Gaussian quadrature in the complex plane?
    Saylor, P. E.; Smolarski, D. C.
    Numerical Algorithms, 2001, vol. 26, no. 3, pp. 251-280, Ingenta.  
  9. Gaussian interval quadrature formula
    Bojanov, B. D.; Petrov, P. P.
    Numerische Mathematik, 2001, vol. 87, no. 4, pp. 625-644, Ingenta.  
  10. 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.  
  11. Stopping functionals for Gaussian quadrature formulas
    Ehrich, S.
    Journal of Computational and Applied Mathematics, 2001, vol. 127, no. ER1-2, pp. 153-171, Ingenta.  
  12. Stopping functionals for Gaussian quadrature formulas   
    Ehrich, Sven   
    Numerical analysis 2000, Vol. V, Quadrature and orthogonal polynomials. J. Comput. Appl. Math. 127 (2001), no. 1-2, 153--171, Math. Sci. Net.  
  13. Convergence of Gaussian quadrature formulas   
    Shi, Ying Guang
    J. Approx. Theory 105 (2000), no. 2, 279--291, Math. Sci. Net.  
  14. Valuing American Put Options Using Gaussian Quadrature.
    Sullivan, Michael A.
    Review of Financial Studies, 2000, vol. 13, no. 1, pp. 75, Ingenta.  
  15. Generalized Gaussian quadrature formulas with Chebyshev nodes  
    Shi, Ying-guang
    J. Comput. Math. 17 (1999), no. 2, 171--178, Math. Sci. Net.  
  16. Accurate recovery of recursion coefficients from Gaussian quadrature formulas.
    Laurie, D.P.
    Journal of Computational and Applied Mathematics, 1999, vol. 112, no. 1/2, pp. 165, Ingenta.  
  17. Efficient Numerical Integration Using Gaussian Quadrature.
    Place, J.; Stach, J.
    Simulation, 1999, vol. 73, no. 4, pp. 232, Ingenta.  
  18. Convergence of Gaussian quadrature and Lagrange interpolation in Haar systems.
    Perez-Acosta, F.; Santos-Leon, J.C.
    BIT, 1999, vol. 39, no. 3, pp. 579, Ingenta.  
  19. Bounds for the third Peano constants of Gaussian quadrature formulae.
    Petras, K.
    Acta mathematica Hungarica, 1999, vol. 83, no. 3, pp. 241, Ingenta.  
  20. Gaussian quadrature rules and numerical examples for strong extensions of mass distribution functions.
    Gustafson, P.E.; Hagler, B.A.
    Journal of Computational and Applied Mathematics, 1999, vol. 105, no. 1/2, pp. 317, Ingenta.  
  21. On Gaussian Quadrature Formulas for the Chebyshev Weight.
    Shi, Ying Guang
    Journal of approximation theory, 1999, vol. 98, no. 1, pp. 183, Ingenta.  
  22. A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network.
    Ghomi, S.M.T. Fatemi; Hashemin, S.S.
    European journal of operational research, 1999, vol. 114, no. 3, pp. 610, Ingenta.  
  23. Evaluations of Hypersingular Integrals using Gaussian Quadrature.
    Hui, C.-Y.; Shia, D.
    International journal for numerical methods in e, 1999, vol. 44, no. 2, pp. 205, Ingenta.  
  24. A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations.
    Ezzirani, Abdelkrim; Guessab, Allal
    Mathematics of computation, 1999, vol. 68, no. 225, pp. 217, Ingenta.  
  25. Optimal sensor placement via Gaussian quadrature  
    Miller, Robert E.
    Appl. Math. Comput. 97 (1998), no. 1, 71--97, Math. Sci. Net.  
  26. General Gaussian quadrature formulas on Chebyshev nodes  
    Shi, Yingguang   
    Adv. Math. (China) 27 (1998), no. 3, 227--239, Math. Sci. Net.  
  27. Gaussian quadrature of Chebyshev polynomials  
    Hunter, D. B.; Nikolov, Geno
    J. Comput. Appl. Math. 94 (1998), no. 2, 123--131, Math. Sci. Net.  
  28. Solving Singular Integral Equations Using Gaussian Quadrature and Overdetermined System.
    Kim, S.
    Computers & mathematics with applications, 1998, vol. 35, no. 10, pp. 63, Ingenta.  
  29. Numerical integration over a disc. A new Gaussian quadrature formula.
    Bojanov, B.; Petrova, G.
    Numerische mathematik, 1998, vol. 80, no. 1, pp. 39, Ingenta.  
  30. Computation of Orientational Averages in Solid-State NMR by Gaussian Spherical Quadrature.
    Eden, Mattias; Levitt, Malcolm H.
    Journal of magnetic resonance, 1998, vol. 132, no. 2, pp. 220, Ingenta.  
  31. Gaussian quadrature and acceleration of convergence  
    Kzaz, M.  
    Numer. Algorithms 15 (1997), no. 1, 75--89, Math. Sci. Net.  
  32. Electrostatic interaction energies from a generalized Gaussian quadrature.
    Cioslowski, J.; Liu, G.
    Chemical physics letters, 1997, vol. 277, no. 4, pp. 299, Ingenta.  
  33. 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.  
  34. Anti-Gaussian Quadrature Formulas  
    Dirk P. Laurie  
    Mathematics of Computation, Vol. 65, No. 214. (Apr., 1996), pp. 739-747, Jstor.  
  35. 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.  
  36. Gaussian Quadrature for Products of Exponential Functions.
    Cordero, M.; Martin, C.; Miller, J.
    Applied mathematics and computation, 1996, vol. 79, no. 2/3, pp. 189, Ingenta.  
  37. An asymptotic expansion for the weights of Gaussian quadrature formulae.
    Petras, K.
    Acta mathematica Hungarica, 1996, vol. 70, no. 1/2, pp. 89, Ingenta.  
  38. Peano kernels and bounds for the error constants of Gaussian and related quadrature rules for Cauchy principal value integrals.
    Diethelm, K.
    Numerische mathematik, 1996, vol. 73, no. 1, pp. 53, Ingenta.  
  39. Gaussian quadrature for matrix valued functions on the real line.
    Sinap, A.
    Journal of computational and applied mathematics, 1995, vol. 65, no. 1/3, pp. 369, Ingenta.  
  40. Gaussian quadrature formulae of the kind for Cauchy principal value integrals: Basic properties and error estimates.
    Diethelm, K.
    Journal of computational and applied mathematics, 1995, vol. 65, no. 1/3, pp. 97, Ingenta.  
  41. Generalized Gaussian Birkhoff Quadrature Formulas.
    Shi, Ying Guang
    Journal of approximation theory, 1995, vol. 82, no. 3, pp. 392, Ingenta.  
  42. Synthesis of Extremal Wavelet-Generating Filters Using Gaussian Quadrature.
    Aas, K.C.; Duell, K.A.; Mullis, C.T.
    IEEE transactions on signal processing, 1995, vol. 43, no. 5, pp. 1045, Ingenta.  
  43. Some error expansions for Gaussian quadrature.
    Hunter, D.B.
    BIT, 1995, vol. 35, no. 1, pp. 64, Ingenta.  
  44. Transfer Probability Calculation for Square Pin Cells by Two-Dimensional Gaussian Quadrature.
    Thomsen, K.L.
    Nuclear science and engineering, 1995, vol. 119, no. 3, pp. 153, Ingenta.  
  45. 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.  
  46. Adaptive Gaussian Integration with the HP48S  
    Lyndell M. Kerley  
    Math. Comput. Ed. 27 (1993), no. 1, 206--214.   
  47. 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.  
  48. Exit criteria and monotonicity in compound quadrature of Gaussian type.
    Forster, K.-J.
    Numerische mathematik, 1993, vol. 66, no. 3, pp. 321, Ingenta.  
  49. Calculation of the Fundamental Mode Sizes in Optical Channel Waveguides
    Using Gaussian Quadrature.
    Jaeger, N.A.F.; Tsou, B.P.C.
    IEEE transactions on microwave theory and techni, 1993, vol. 41, no. 11, pp. 1907, Ingenta.  
  50. Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle [CAM 1335].
    Gragg, W.B.
    Journal of computational and applied mathematics, 1993, vol. 46, no. 1/2, pp. 183, Ingenta.  
  51. 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.  
  52. 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.  
  53. The numerical solution of inverse problems using Gaussian quadrature.
    Narayanan, K.S.S.; Ramadurai, K.S.
    European journal of physics, 1992, vol. 13, no. 3, pp. 111, Ingenta.  
  54. Gaussian Quadrature for Trigonometric Polynomials: An Example from Observability.
    Gilliam, David; Martin, Clyde F.; Lund, John
    Applicable analysis, 1992, vol. 44, no. 3/4, pp. 183, Ingenta.  
  55. A Note on the Error in Gaussian Quadrature.
    Martin, Clyde
    Applied mathematics and computation, 1992, vol. 47, no. 1, pp. 25, Ingenta.  
  56. 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.  
  57. A Gaussian quadrature for the calculation of generalized Fermoi-Dirac integrals.
    Sagar, R.P.
    Computer physics communications, 1991, vol. 66, no. 2/3, pp. 271, Ingenta.  
  58. A Gaussian quadrature for the optimal evaluation of integrals involving Lorentzians over a semi-infinite interval.
    Sagar, R.P.; Smith, Jr., V.H.; Simas, A.M.
    Computer physics communications, 1991, vol. 62, no. 1, pp. 16, Ingenta.  
  59. 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.  
  60. The Error Norm of Gaussian Quadrature Formulae for Weight Functions of Bernstein-Szego Type.
    Notaris, S.E.
    Numerische mathematik, 1990, vol. 57, no. 3, pp. 271, Ingenta.  
  61. Quadrature Formulas Associated with Divisors of the Field of Gaussian Numbers.
    Voronin, S.M.; Temirgaliev, N.
    Mathematical notes of the Academy of Sciences of the USSR, 1989, vol. 46, no. 1/2, pp. 597, Ingenta.  
  62. Remarks on convergence of gaussian quadrature for singular integrals.
    Vertesi, P.
    Acta mathematica Hungarica, 1989, vol. 53, no. 3/4, pp. 399, Ingenta.  
  63. Error bounds for quadrature formulas near Gaussian quadrature.
    Brass, H.; Forster, K.-J.
    Journal of computational and applied mathematics, 1989, vol. 28, pp. 145, Ingenta.  
  64. Gaussian-like quadrature rules for quantum mechanical calculations.
    Linderberg, Jan; Ohrn, Yngve; Padkjaer, Soren B.
    The journal of chemical physics, 1989, vol. 91, no. 8, pp. 4793, Ingenta.  
  65. Existence of Gaussian Quadrature formulas for Birkhoff type data.
    Dyn, N.
    Archiv der Mathematik, 1989, vol. 52, no. 6, pp. 588, Ingenta.  
  66. On Kutt's Gaussian quadrature rule for finite-part integrals.
    Ioakimidis, N. I.
    Applied numerical mathematics, 1989, vol. 5, no. 3, pp. 209, Ingenta.  
  67. On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals.
    Criscuolo, G.; Mastroianni, G.
    Numerische mathematik, 1989, vol. 54, no. 4, pp. 445, Ingenta.  
  68. Gaussian quadrature formulae with fixed nodes
    Johnson, Diane L.
    J. Approx. Theory 53 (1988), no. 3, 239--250, Math. Sci. Net.  
  69. The use of Gaussian Quadrature formulas when solving diffraction Problems on the Basis of the Magnetic Field Integral Equation.
    Ankudinov, V.Ye.; Romanov, Ye.A.
    Soviet journal of communications technology & el, 1988, vol. 33, no. 10, pp. 31, Ingenta.  
  70. Proof without Words: The Gaussian Quadrature as the Area of Either Trapezoid  
    Mike Akerman  
    Mathematics Magazine: Volume 60, Number 2, (1987), Page: 89.   
  71. The Error Norm of Certain Gaussian Quadrature Formulae  
    G. Akrivis  
    Mathematics of Computation, Vol. 45, No. 172. (Oct., 1985), pp. 513-519, Jstor.  
  72. 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.  
  73. Composite Hermite-Birkhoff Quadrature Formulas of Gaussian Type  
    Nira Dyn  
    Mathematics of Computation, Vol. 43, No. 168. (Oct., 1984), pp. 535-541, Jstor.  
  74. 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.  
  75. 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.  
  76. 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.  
  77. 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.  
  78. Asymptotic Error Estimates for Gaussian Quadrature Formulas  
    T. H. Charles Chen  
    Mathematics of Computation, Vol. 38, No. 157. (Jan., 1982), pp. 143-152, Jstor.  
  79. Quadratic Integration of Gaussian Processes  
    T. F. Lin  
    Proceedings of the American Mathematical Society, Vol. 81, No. 4. (Apr., 1981), pp. 618-623, Jstor.  
  80. 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.  
  81. On Multiple Node Gaussian Quadrature Formulae  
    David L. Barrow  
    Mathematics of Computation, Vol. 32, No. 142. (Apr., 1978), pp. 431-439, Jstor.  
  82. 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.  
  83. A Note on Extended Gaussian Quadrature Rule  
    Giovanni Monegato  
    Mathematics of Computation, Vol. 30, No. 136. (Oct., 1976), pp. 812-81, Jstor.  
  84. 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.  
  85. Numerical Construction of Gaussian Quadrature Formulas  
    Bernard Danloy
    Mathematics of Computation, Vol. 27, No. 124. (Oct., 1973), pp. 861-869, Jstor.  
  86. Concerning Gaussian-Chebyshev Quadrature Errors  
    Charles K. Chui  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 237-240, Jstor.  
  87. 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.  
  88. Trigonometric and Gaussian Quadrature  
    C. J. Knight, A. C. R. Newbery  
    Mathematics of Computation, Vol. 24, No. 111. (Jul., 1970), pp. 575-581, Jstor.  
  89. 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.  
  90. 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.  
  91. 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.  
  92. 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.  
  93. 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.  
  94. 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.  
  95. 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.  
  96. 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.  
  97. 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.  
  98. 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.  
  99. 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.  
  100. Convergence properties of Gaussian quadrature formulae.
    Barrett, W.
    Comput. J. 3 (1960/1961) 272--277, Math. Sci. Net.  
  101. 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.  
  102. Abscissas and weights for Gaussian quadratures of high order  
    Davis, P.; Rabinowitz, P.  
    J. Res. Nat. Bur. Standards 56 (1956), 35--37, Math. Sci. Net.  

 

 

 

 

 

 

 

 

 

 

 

 

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