Bibliography

for

Adaptive Simpson's Rule

Return to Numerical Methods - Numerical Analysis

 

  1. The utilisation of an adaptive 3D Gauss-Legendre quadrature in the simulation of sound propagation outdoors for sources with variable power distribution
    Abdullah, S.; Nor, M. J.
    Applied Acoustics, 2001, vol. 62, no. ER1, pp. 65-83 , Ingenta.  
  2. The Utilisation of an Adaptive 3D Gauss-Legendre Quadrature in the Simulation of Sound Propagation Outdoors for Sources with Variable Power Distribution
    Noise and Vibration Bulletin, 2001, no. FEB, pp. 32 , Ingenta.  
  3. Adaptive quadrature---revisited   
    Gander, Walter; Gautschi, Walter
    BIT 40 (2000), no. 1, 84--101, MathSciNet.  
  4. Self-adaptive quadrature and numerical path integration.
    Sabo, Dubravko; Doll, J. D.; Freeman, David L.
    Journal of Chemical Physics, 2000, vol. 113, no. 7, pp. 2522 , Ingenta.  
  5. Adaptive differential quadrature element refinement analyses of fluid mechanics problems.
    Chen, C.-N.
    Computer methods in applied mechanics and engineering, 1999, vol. 180, no. 1/2, pp. 47 , Ingenta.  
  6. Application of Adaptive Quadrature to Fire Radiation Modeling.
    Cumber, P.S.
    Journal of heat transfer, 1999, vol. 121, no. 1, pp. 203 , Ingenta.  
  7. A hybrid subdivision strategy for adaptive integration routines   
    Cools, Ronald; Maerten, Bart  
    J. UCS 4 (1998), no. 5, 486--500 (electronic), MathSciNet.  
  8. Application of Adaptive Quadrature to Axi-symmetric Vortex Sheet Motion.
    Nie, Qing; Baker, Greg
    Journal of computational physics, 1998, vol. 143, no. 1, pp. 49 , Ingenta.  
  9. Adaptive quadrature filters for multiple phase-stepping images.
    Marroquin, J.L.; Servin, M.; Vera, R. Rodriguez
    Optics letters, 1998, vol. 23, no. 4, pp. 238 , Ingenta.  
  10. On quasi-Monte Carlo integrations   
    Sobol, I. M.  
    IMACS Seminar on Monte Carlo Methods (Brussels, 1997). Math. Comput. Simulation 47 (1998), no. 2-5, 103--112, Math. Sci. Net.   
  11. Local error estimates and regularity tests for the implementation of double adaptive quadrature   
    Favati, Paola; Fiorentino, Giuseppe; Lotti, Grazia; Romani, Francesco
    ACM Trans. Math. Software 23 (1997), no. 1, 16--31, MathSciNet.  
  12. Bisection method for Monte Carlo integration   
    Okamoto, Masashi; Takahashi, Rinya
    Math. Japon. 22 (1977), no. 3, 403--411, Math. Sci. Net.   
  13. Subregion-adaptive integration of functions having a dominant peak   
    Genz, Alan; Kass, Robert E.
    J. Comput. Graph. Statist. 6 (1997), no. 1, 92--111, MathSciNet.  
  14. Adaptive quadrature filters and the recovery of phase from fringe pattern images.
    Marroquin, J.L.; Servin, M.; Rodriguez-Vera, R.
    Journal of the Optical Society of America. A, Optics, image science, and vision., 1997, vol.
    14, no. 8, pp. 1742 , Ingenta.  
  15. Local Error Estimates and Regularity Tests for the Implementation of Double Adaptive Quadrature.
    Favati, Paola; Fiorentino, Giuseppe; Romani, Francesco
    Acm transactions on mathematical software, 1997, vol. 23, no. 1, pp. 16 , Ingenta.  
  16. Error bounds for quasi-Monte Carlo integration with nets   
    Lécot, Christian  
    Math. Comp. 65 (1996), no. 213, 179--187, Math. Sci. Net.   
  17. Adaptive integration techniques for almost singular functions in the boundary element method  
    Karafiat, A.  
    Comput. Math. Appl. 32 (1996), no. 5, 11--30, MathSciNet.  
  18. Adaptive Finite Element Methods for Parabolic Problems V: Long-Time Integration  
    Kenneth Eriksson, Claes Johnson  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 6. (Dec., 1995), pp. 1750-1763, Jstor.  
  19. The optimal error of Monte Carlo integration   
    Mathé, Peter  
    J. Complexity 11 (1995), no. 4, 394--415, Math. Sci. Net.   
  20. Parallel globally adaptive quadrature on the KSR-1   
    Bull, J. M.; Freeman, T. L.  
    Adv. Comput. Math. 2 (1994), no. 4, 357--373, MathSciNet.  
  21. Adaptive Gaussian Integration with the HP48S  
    Kerley, Lyndell M.  
    Mathematics and computer education, 1993, vol. 27, no. 3, pp. 206 , Ingenta.  
  22. Adaptive Quadrature on a Message-Passing Multiprocessor.
    Miller, Valerie; Davis, George J.
    Journal of parallel and distributed computing, 1992, vol. 14, no. 4, pp. 417 , Ingenta.  
  23. Some stability aspects of schemes for the adaptive integration of stiff initial value problems   
    Dieci, Luca; Estep, Donald  
    SIAM J. Sci. Statist. Comput. 12 (1991), no. 6, 1284--1303, MathSciNet.  
  24. On the subdivision strategy in adaptive quadrature algorithms.
    Berntsen, J.; Espelid, T.O.; Sorevik, T.
    Journal of computational and applied mathematics, 1991, vol. 35, pp. 119 , Ingenta.  
  25. Parallel systems and adaptive integration. Statistical multiple integration  
    de Doncker, E.; Kapenga, J. A.
    (Arcata, CA, 1989), 33--51,  Contemp. Math., 115, Amer. Math. Soc., Providence, RI, 1991, MathSciNet.  
  26. Adaptive quadratures over volumes  
    Georg, K.; Widmann, R.  
    Computing 47 (1991), no. 2, 121--136, MathSciNet.  
  27. On the construction of high-order integration formulae for the adaptive quadrature method  
    Sugiura, Hiroshi; Sakurai, Tetsuya
    Proceedings of the 3rd International Congress on Computational and Applied Mathematics (Leuven, 1988). J. Comput. Appl. Math. 28 (1989), Special Issue, 367--381, MathSciNet.  
  28. A discussion of a new error estimate for adaptive quadrature  
    Espelid, Terje O.; Sørevik, Tor  
    BIT 29 (1989), no. 2, 283--294, MathSciNet.  
  29. Practical error estimation in adaptive multidimensional quadrature routines.
    Bernsten, J.
    Journal of computational and applied mathematics, 1989, vol. 25, no. 3, pp. 327 , Ingenta.  
  30. Performance of self-validating adaptive quadrature  
    Corliss, George F.  
    Numerical integration (Halifax, N.S., 1986), 239--259, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 203, Reidel, Dordrecht, 1987, MathSciNet.  
  31. A parallelization of adaptive integration methods  
    de Doncker, Elise; Kapenga, John A.  
    Numerical integration (Halifax, N.S., 1986), 207--218, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 203, Reidel, Dordrecht, 1987, MathSciNet.  
  32. On the subdivision strategy in numerical adaptive integration over the cube  
    Berntsen, Jarle  
    Reports in Informatics, 11. University of Bergen, Department of Informatics, Bergen, 1984. ii+32 pp, MathSciNet.  
  33. Increasing robustness in global adaptive quadrature through interval selection heuristics  
    Shapiro, Henry D.  
    ACM Trans. Math. Software 10 (1984), no. 2, 117--139, MathSciNet.  
  34. An adaptive Simpson quadrature algorithm for learning purposes   
    D. Katsifli  and  D. J. Fyfe   
    Int. J. Math. Educ. Sci. Technol.,Vol. 14, No. 3, (1983), pp. 341-350.   
  35. Extrapolated adaptive quadrature   
    Kahaner, D.; Stoer, J.
    SIAM J. Sci. Statist. Comput. 4 (1983), no. 1, 31--44, MathSciNet.  
  36. Corrigenda: "Double integration using one-dimensional adaptive quadrature routines: a software interface problem"
    Fritsch, F. N.  
    ACM Trans. Math. Software 7 (1981), no. 2, 252, MathSciNet.  
  37. Double integration using one-dimensional adaptive quadrature routines: a software interface problem.
    Fritsch, F. N.; Kahaner, D. K.; Lyness, J. N.    
    ACM Trans. Math. Software 7 (1981), no. 1, 46--75., MathSciNet.  
  38. Improvements of adaptive Newton-Cotes quadrature methods   
    Ninomiya, Ichizo
    J. Inform. Process. 3 (1980/81), no. 3, 162--170, MathSciNet.  
  39. An alternative strategy for cautious adaptive quadrature   
    Hazlewood, L. J.  
    J. Inst. Math. Appl. 20 (1977), no. 4, 505--518, MathSciNet.  
  40. Parallel algorithms for adaptive quadrature. III. Program correctness  
    Rice, John R.
    ACM Trans. Math. Software 2 (1976), no. 1, 1--30, MathSciNet.  
  41. Adaptive Integration and Improper Integrals  
    Seymour Haber  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 806-809, Jstor.  
  42. A metalgorithm for adaptive quadrature  
    Rice, John R.  
    J. Assoc. Comput. Mach. 22 (1975), 61--82, MathSciNet.  
  43. Adaptive quadrature: convergence of parallel and sequential algorithms
    Rice, John R.
    Bull. Amer. Math. Soc. 80 (1974), 1250--1254, MathSciNet.  
  44. A technique for analysing adaptive quadrature strategies  
    Simpson, R. B.
    Proceedings of the Third Manitoba Conference on Numerical Mathematics (Winnipeg, Man., 1973), pp. 369--378, MathSciNet.  
  45. Adaptive integration and improper integrals   
    Haber, Seymour  
    Math. Comp. 29 (1975), 806--809, MathSciNet.  
  46. Notes on the adaptive Simpson quadrature routine.
    Lyness, J. N.
    J. Assoc. Comput. Mach. 16 1969 483--495, MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003