Bibliography for the Cauchy Principal Value

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  1. Sigmoidal-trapezoidal quadrature for ordinary and Cauchy principal value integrals.
    Elliott, David
    ANZIAM J. 46 (2004), (E), E1--E69, MathSciNet.  
  2. A note on the stability analysis of a quadrature rule of interpolatory type for Cauchy principal value integrals.
    Kim, Philsu; Ahn, Soyoung; Choi, U Jin
    Int. Math. J. 3 (2003), no. 8, 825--835, MathSciNet.  
  3. Two general methods for the numerical approximation of multidimensional Cauchy principal value integrals  PDF  
    Kai Diethelm
    Anziam J., Vol. 42 , (2000/01), (E), pp. E1- E26, MathSciNet.  
  4. Uniform Convergence Results For Certain Two-Dimensional Cauchy Principal Value Integrals  PDF  
    Elisabetta Santi
    Portugaliæ Mathematica,Vol. 57, No. 2, (2000), pp. 191-201, MathSciNet.  
  5. Principal values for the Cauchy integral and rectifiability.
    Tolsa, Xavier
    Proc. Amer. Math. Soc. 128 (2000), no. 7, 2111--2119, MathSciNet.  
  6. Computation of the Cauchy principal value integrals on the real line.
    De Bonis, M. C.; Russo, M. G.
    Advanced special functions and applications (Melfi, 1999), 197--210, Proc. Melfi Sch. Adv. Top. Math. Phys., 1, Aracne, Rome, 2000, MathSciNet.  
  7. Axisymmetric Vortex Sheet Motion: Accurate Evaluation of the Principal Value Integral  PDF  
    Monika Nitsche
    SIAM Journal on Scientific Computing, Volume 21, Number 3, (1999), pp. 1066-1084
  8. An Error Analysis of the Cauchy Principal Value Integral Evaluation by the IMT Scheme
    N. Mohankumar; A. Natarajan
    Proceedings: Mathematical, Physical and Engineering Sciences, Vol. 454, No. 1968 (Jan., 1998), pp. 139-145, Jstor.  
  9. Cauchy principal value integral using hybrid integral  
    Hiroshi Kai; Matu-Tarow Noda  
    ACM SIGSAM Bulletin, Volume 31 ,  Issue 3  (September 1997), pp. 37-38.  
  10. Cauchy's principal value of local times of Lévy processes with no negative jumps via continuous branching processes  
    Jean Bertoin
    Electronic J. of Probability, Vol. 2,  (1997), Paper No. 6, pp. 1-12.
  11. New method for the numerical calculation of Cauchy principal value integrals in BEM applied to electromagnetics
    Huber, C.J.; Rucker, W.M.; Hoschek, R.; Richter, K.R.
    IEEE Transactions on Magnetics, v 33, n 2 pt 2, Mar, 1997, p 1386-1389, Compendex.
  12. The Use of Spline-on-Spline for the Approximation of Cauchy Principal Value Integrals
    Behforooz G.H.
    Applied Mathematics and Computation, November 1996, vol. 80, no. 1, pp. 23-32(10), Ingenta.
  13. Evaluations of Cauchy principal value integrals and weakly singular integrals in BEM and their applications
    Zhu, J.; Shah, A.H.; Datta, S.K.
    International Journal for Numerical Methods in Engineering, v 39, n 6, Mar 30, 1996, p 1017-1028, Compendex.
  14. The Continuation Approach: A General Framework for the Analysis and Evaluation of Singular and Near-Singular Integrals
    Dan Rosen; Donald E. Cormack
    SIAM Journal on Applied Mathematics, Vol. 55, No. 3 (Jun., 1995), pp. 723-762, Jstor.  
  15. Gaussian quadrature formulae of the third kind for Cauchy principal value integrals: Basic properties and error estimates
    Diethelm K.
    Journal of Computational and Applied Mathematics, 29 December 1995, vol. 65, no. 1, pp. 97-114(18), Ingenta.
  16. The Numerical Evaluation of a 2-D Cauchy Principal Value Integral Arising in Boundary Integral Equation Methods
    Giovanni Monegato
    Mathematics of Computation, Vol. 62, No. 206 (Apr., 1994), pp. 765-777, Jstor.  
  17. A Comparison of Some Quadrature Methods for Approximating Cauchy Principal Value Integrals
    Natarajan, A.; Mohankumar, N.
    Journal of Engineering Design, v 516, n 4, 1994, p 365, Compendex.
  18. Singular and Near Singular Integrals in the Bem: A Global Approach
    Dan Rosen; Donald E. Cormack
    SIAM Journal on Applied Mathematics, Vol. 53, No. 2 (Apr., 1993), pp. 340-357, Jstor.  
  19. Infinite boundary elements with direct evaluation of Cauchy principal value integrals
    Parreira, P.; Pereira, Almeida O.J.B.
    Boundary Elements XV: Fluid Flow and Computational Aspects, 1993, p 469-482, Compendex.
  20. Numerical computation of complex Cauchy principal value integrals
    Acharya, B.P.; Mahapatra, T.
    International Journal of Computer Mathematics, v 43, n 3-4, 1992, p 147-151, Compendex.
  21. An Automatic Quadrature for Cauchy Principal Value Integrals
    Takemitsu Hasegawa; Tatsuo Torii
    Mathematics of Computation, Vol. 56, No. 194 (Apr., 1991), pp. 741-754, Jstor.  
  22. Uniform Convergence Results for Cauchy Principal Value Integrals
    Philip Rabinowitz
    Mathematics of Computation, Vol. 56, No. 194 (Apr., 1991), pp. 731-740, Jstor.  
  23. The evaluation of Cauchy principal value integrals in the boundary element method---A review
    M. Guiggiani
    Mathematical and Computer Modelling, Special Issue on BIEM/BEM, Vol. 15, No. 3--5, pp. 175--184, 1991.
  24. Generalized Noninterpolatory Rules for Cauchy Principal Value Integrals
    Philip Rabinowitz
    Mathematics of Computation, Vol. 54, No. 189 (Jan., 1990), pp. 271-279, Jstor.  
  25. Numerical Evaluation of Cauchy Principal Value Integrals with Singular Integrands
    Philip Rabinowitz
    Mathematics of Computation, Vol. 55, No. 191 (Jul., 1990), pp. 265-276, Jstor.  
  26. A Sinc-Hunter Quadrature Rule for Cauchy Principal Value Integrals
    Bernard Bialecki
    Mathematics of Computation, Vol. 55, No. 192 (Oct., 1990), pp. 665-681, Jstor.  
  27. Noninterpolatory Integration Rules for Cauchy Principal Value Integrals
    P. Rabinowitz; D. S. Lubinsky
    Mathematics of Computation, Vol. 53, No. 187 (Jul., 1989), pp. 279-295, Jstor.  
  28. On the Convergence of Product Formulas for the Evaluation of Certain Two-Dimensional Cauchy Principal Value Integrals
    Giuseppe Mastroianni
    Mathematics of Computation, Vol. 52, No. 185 (Jan., 1989), pp. 95-101, Jstor.  
  29. Convergence Results for Piecewise Linear Quadratures for Cauchy Principal Value Integrals
    Philip Rabinowitz
    Mathematics of Computation, Vol. 51, No. 184 (Oct., 1988), pp. 741-747, Jstor.  
  30. On the Convergence of Product Formulas for the Numerical Evaluation of Derivatives of Cauchy Principal Value Integrals
    Giuliana Criscuolo; Giuseppe Mastroianni
    SIAM Journal on Numerical Analysis, Vol. 25, No. 3 (Jun., 1988), pp. 713-727, Jstor.  
  31. Sinc-Nystrom Method for Numerical Solution of One-Dimensional Cauchy Singular Integral Equation Given on a Smooth Arc in the Complex Plane
    Bernard Bialecki; Frank Stenger
    Mathematics of Computation, Vol. 51, No. 183 (Jul., 1988), pp. 133-165, Jstor.  
  32. On The Convergence Of A Rule By Monegato For The Numerical Evaluation Of Cauchy Principal Value Integrals.
    Chiodo, Claudia; Crisuolo, Giuliana
    Computing (Vienna/New York), v 40, n 1, 1988, p 67-74, Compendex.
  33. On the solution to a Cauchy principal value integral equation which arises in fracture mechanics  
    A. K. Gautesen; J. Dundurs
    SIAM Journal on Applied Mathematics, Vol. 47, No. 1 (Feb., 1987), pp. 109-116, Jstor.  
  34. Quadrature Formulae for Cauchy Principal Value Integrals of Oscillatory Kind
    G. E. Okecha
    Mathematics of Computation, Vol. 49, No. 179 (Jul., 1987), pp. 259-268, Jstor.  
  35. On the Convergence of an Interpolatory Product Rule for Evaluating Cauchy Principal Value Integrals
    Giuliana Criscuolo; Giuseppe Mastroianni
    Mathematics of Computation, Vol. 48, No. 178 (Apr., 1987), pp. 725-735, Jstor.  
  36. Direct Computation Of Cauchy Principal Value Integrals In Advanced Boundary Elements.
    Guiggiani, Massimo; Casalini, Paolo
    International Journal for Numerical Methods in Engineering, v 24, n 9, Sep, 1987, p 1711-1720, Compendex.
  37. Piecewise-Polynomial Quadratures for Cauchy Singular Integrals
    Apostolos Gerasoulis
    SIAM Journal on Numerical Analysis, Vol. 23, No. 4 (Aug., 1986), pp. 891-902, Jstor.  
  38. 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.  
  39. Computation Of The Roots Of Cauchy Type Principal Value Integrals.
    Anastasselou, Eleni G.  
    International Journal Of Computer Mathematics, V 16, N 1, Aug, 1984, P 85-96, Compendex.
  40. Gauss-Kronrod Integration Rules for Cauchy Principal Value Integrals
    Philip Rabinowitz
    Mathematics of Computation, Vol. 41, No. 163 (Jul., 1983), pp. 63-78, Jstor.  
  41. On approximation of complex Cauchy principal value integrals.
    Acharya, B. P.; Das, R. N.
    J. Orissa Math. Soc. 1 (1982), no. 2, 43--50, MathSciNet.  
  42. Cubic Splines and Approximate Solution of Singular Integral Equations
    Erica Jen; R. P. Srivastav
    Mathematics of Computation, Vol. 37, No. 156 (Oct., 1981), pp. 417-423, Jstor.  
  43. Numerical determination of Cauchy principal value integrals.
    Acharya, B. P.; Das, R. N.
    Computing 27 (1981), no. 4, 373--378, MathSciNet.  
  44. Gauss Type Quadrature Rules for Cauchy Principal Value Integrals
    David Elliott; D. F. Paget
    Mathematics of Computation, Vol. 33, No. 145 (Jan., 1979), pp. 301-309, Jstor.  
  45. The Numerical Solution of Singular Integral Equations Over (-1,1)
    M. L. Dow; David Elliott
    SIAM Journal on Numerical Analysis, Vol. 16, No. 1 (Feb., 1979), pp. 115-134, Jstor.  
  46. Convergence of Fejer type quadrature formulas for Cauchy principal value integrals.
    Chawla, M. M.; Kumar, Sheo
    J. Math. Phys. Sci. 12 (1978), no. 1, 49--59, MathSciNet.  
  47. On Quadrature Rules for Ordinary and Cauchy Principal Value Integrals over Contours
    David Elliott; J. D. Donaldson
    SIAM Journal on Numerical Analysis, Vol. 14, No. 6 (Dec., 1977), pp. 1078-1087, Jstor.  
  48. Automatic Evaluation Of Cauchy Principal Value Integrals.
    Piessens, R.; Van Roy-Branders, M.; Mertens, I.
    Angewandte Informatik/Applied Informatics, V 18, N 1, Jan, 1976, P 31-35, Compendex.
  49. On Finite Hilbert Transforms
    Kevin F. Clancey
    Transactions of the American Mathematical Society, Vol. 212 (Oct., 1975), pp. 347-354, Jstor.  
  50. A theorem on preserving the class H(M,alpha,phi) by a singular integral in the sense of Cauchy's principal value.
    Leksinski, Wacaw; .Zakowski, Wojciech
    Collection of articles in memory of Witold Pogorzelski. Demonstratio Math. 5 (1973), 139--145, MathSciNet.   
  51. Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals.
    Hunter, D. B.
    Numer. Math. 19 (1972), 419--424, MathSciNet.  
  52. Indefinite Integration by Residues
    R. P. Boas, Jr.; Lowell Schoenfeld
    SIAM Review, Vol. 8, No. 2 (Apr., 1966), pp. 173-183, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006