메뉴 건너뛰기




Volumn 38, Issue 2, 1998, Pages 256-274

The numerical evaluation of cauchy principal value integrals with non-standard weight functions

Author keywords

Cauchy principal value integrals; Convergence; Quadrature rules

Indexed keywords


EID: 0042359711     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02512366     Document Type: Article
Times cited : (5)

References (31)
  • 1
    • 0002141721 scopus 로고
    • On the convergence of the Gauss quadrature rules for Cauchy principal value integrals
    • G. Criscuolo and G. Mastroianni, On the convergence of the Gauss quadrature rules for Cauchy principal value integrals, Ricerche di Matematica, 35 (1986), pp. 45-60.
    • (1986) Ricerche di Matematica , vol.35 , pp. 45-60
    • Criscuolo, G.1    Mastroianni, G.2
  • 2
    • 51249176117 scopus 로고
    • Convergenza di formule Gaussiane per il calcolo delle derivate di integrali a valor principale secondo Cauchy
    • G. Criscuolo and G. Mastroianni, Convergenza di formule Gaussiane per il calcolo delle derivate di integrali a valor principale secondo Cauchy, Calcolo, 24 (1987), pp. 179-192.
    • (1987) Calcolo , vol.24 , pp. 179-192
    • Criscuolo, G.1    Mastroianni, G.2
  • 3
    • 84966225697 scopus 로고
    • On the convergence of an interpolatory product rule for evaluating Cauchy principal value integrals
    • G. Criscuolo and G. Mastroianni, On the convergence of an interpolatory product rule for evaluating Cauchy principal value integrals, Math. Comp., 48 (1987), pp. 725-735.
    • (1987) Math. Comp. , vol.48 , pp. 725-735
    • Criscuolo, G.1    Mastroianni, G.2
  • 4
    • 0000357289 scopus 로고
    • On the convergence of product formulas for the numerical evaluation of derivatives of Cauchy principal value integrals
    • G. Criscuoloand G. Mastroianni, On the convergence of product formulas for the numerical evaluation of derivatives of Cauchy principal value integrals, SIAM J. Numer. Anal., 25 (1988), pp. 713-727.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 713-727
    • Criscuoloand, G.1    Mastroianni, G.2
  • 5
    • 0009934465 scopus 로고
    • On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals
    • G. Criscuolo and G. Mastroianni, On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals, Numer. Math., 54, (1989), pp. 145-161.
    • (1989) Numer. Math. , vol.54 , pp. 145-161
    • Criscuolo, G.1    Mastroianni, G.2
  • 6
    • 0039469309 scopus 로고
    • Mean and uniform convergence of quadrature rules for evaluating the finite Hilbert transform
    • P. Nevai and A. Pinkus, eds., Academic Press, New York
    • G. Criscuolo and G. Mastroianni, Mean and uniform convergence of quadrature rules for evaluating the finite Hilbert transform, in P. Nevai and A. Pinkus, eds., Progress in Approximation Theory-A special volume of J. Approx. Theory, Academic Press, New York, 1991, pp. 141-176.
    • (1991) Progress in Approximation Theory-A Special Volume of J. Approx. Theory , pp. 141-176
    • Criscuolo, G.1    Mastroianni, G.2
  • 7
    • 0346499989 scopus 로고
    • Lagrange interpolation on generalized Jacobi zeros with additional nodes
    • G. Criscuolo and G. Mastroianni, Lagrange interpolation on generalized Jacobi zeros with additional nodes, Acta Mathematica Hungarica, 65 (1994), pp. 27-49.
    • (1994) Acta Mathematica Hungarica , vol.65 , pp. 27-49
    • Criscuolo, G.1    Mastroianni, G.2
  • 8
    • 0003774710 scopus 로고
    • Associated generalized Jacobi functions and polynomials
    • G. Criscuolo, G. Mastroianni, and P. Nevai, Associated generalized Jacobi functions and polynomials, J. Math. Anal. Applic., 158:1 (1991), pp. 15-34.
    • (1991) J. Math. Anal. Applic. , vol.158 , Issue.1 , pp. 15-34
    • Criscuolo, G.1    Mastroianni, G.2    Nevai, P.3
  • 10
    • 0345869169 scopus 로고
    • On the evaluation of certain two-dimensional singular integrals with Cauchy kernels
    • C. Dagnino-and A. Palamara Orsi, On the evaluation of certain two-dimensional singular integrals with Cauchy kernels, Numer. Math., 46 (1985), pp. 121-130.
    • (1985) Numer. Math. , vol.46 , pp. 121-130
    • Dagnino, C.1    Palamara Orsi, A.2
  • 11
    • 0006033397 scopus 로고
    • The numerical evaluation of principal value integrals
    • L. M. Delves, The numerical evaluation of principal value integrals, Computing, 10 (1968), pp. 389-391.
    • (1968) Computing , vol.10 , pp. 389-391
    • Delves, L.M.1
  • 12
    • 0001039575 scopus 로고
    • On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals
    • D. Elliott and D. F. Paget, On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals, Numer. Math., 23 (1975), pp. 311-319.
    • (1975) Numer. Math. , vol.23 , pp. 311-319
    • Elliott, D.1    Paget, D.F.2
  • 13
    • 0001008193 scopus 로고
    • On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals: An addendum
    • D. Elliott and D. F. Paget, On the convergence of a quadrature rule for evaluating certain Cauchy principal value integrals: An addendum, Numer. Math., 25 (1976), pp. 287-289.
    • (1976) Numer. Math. , vol.25 , pp. 287-289
    • Elliott, D.1    Paget, D.F.2
  • 14
    • 84968513278 scopus 로고
    • Gauss type quadrature rules for Cauchy principal value integrals
    • D. Elliott and D. F. Paget, Gauss type quadrature rules for Cauchy principal value integrals, Math. Comp., 33 (1979), pp. 301-309.
    • (1979) Math. Comp. , vol.33 , pp. 301-309
    • Elliott, D.1    Paget, D.F.2
  • 15
    • 84966226823 scopus 로고
    • On some orthogonal polynomial integrals
    • L. Gatteschi, On some orthogonal polynomial integrals, Math. Comp., 35, (1980), pp. 1291-1298.
    • (1980) Math. Comp. , vol.35 , pp. 1291-1298
    • Gatteschi, L.1
  • 16
    • 0001054517 scopus 로고
    • On the construction of Gaussian rules from modified moments
    • W. Gautschi, On the construction of Gaussian rules from modified moments, Math. Comp., 24 (1970), pp. 245-260.
    • (1970) Math. Comp. , vol.24 , pp. 245-260
    • Gautschi, W.1
  • 17
    • 0038907613 scopus 로고
    • A survey of Gauss-Christoffel quadrature formulae
    • E. B. Christoffel; the influence of his work Internat. Christoffel Symposium. A collection of articles in honour of Christoffel on the 150th anniversary of his birth, P. L. Butzer and F. Fehr, eds., Birkhäuser Verlag, Basel
    • W. Gautschi, A survey of Gauss-Christoffel quadrature formulae, in E. B. Christoffel; the influence of his work in Mathematics and Physical Sciences. Internat. Christoffel Symposium. A collection of articles in honour of Christoffel on the 150th anniversary of his birth, P. L. Butzer and F. Fehr, eds., Birkhäuser Verlag, Basel, 1981.
    • (1981) Mathematics and Physical Sciences
    • Gautschi, W.1
  • 19
    • 0001287058 scopus 로고
    • Some Gauss type formula the evaluation of Cauchy principal value of integrals
    • D. B. Hunter, Some Gauss type formula the evaluation of Cauchy principal value of integrals, Numer. Math., 19 (1972), pp. 419-424.
    • (1972) Numer. Math. , vol.19 , pp. 419-424
    • Hunter, D.B.1
  • 20
    • 84966223682 scopus 로고
    • On the convergence of product formulas for the evaluation of certain two-dimensional Cauchy principal value integrals
    • G. Mastroianni, On the convergence of product formulas for the evaluation of certain two-dimensional Cauchy principal value integrals, Math. Comp., 52 (1989), pp. 95-101.
    • (1989) Math. Comp. , vol.52 , pp. 95-101
    • Mastroianni, G.1
  • 21
    • 0030167791 scopus 로고    scopus 로고
    • Some numerical algorithms to evaluate the Hadamard finite part integrals
    • N. Mastronardi and D. Occorsio, Some numerical algorithms to evaluate the Hadamard finite part integrals, J. Comput. Appl. Math., 70 (1996), pp. 75-93.
    • (1996) J. Comput. Appl. Math. , vol.70 , pp. 75-93
    • Mastronardi, N.1    Occorsio, D.2
  • 22
    • 0001482088 scopus 로고
    • The numerical evaluation of one-dimensional Cauchy principal value integrals
    • G. Monegato, The numerical evaluation of one-dimensional Cauchy principal value integrals, Computing, 29 (1982), pp. 337-354.
    • (1982) Computing , vol.29 , pp. 337-354
    • Monegato, G.1
  • 23
    • 0001516384 scopus 로고
    • Convergence of product formulas for the numerical evaluation of certain two-dimensional Cauchy principal integrals
    • G. Monegato, Convergence of product formulas for the numerical evaluation of certain two-dimensional Cauchy principal integrals, Numer. Math., 43 (1984), pp. 161-173.
    • (1984) Numer. Math. , vol.43 , pp. 161-173
    • Monegato, G.1
  • 24
    • 0000762664 scopus 로고
    • Mean convergence of Lagrange interpolation. III
    • P. Nevai, Mean convergence of Lagrange interpolation. III, Trans. Amer. Math. Soc., 282 (1984), pp. 669-698.
    • (1984) Trans. Amer. Math. Soc. , vol.282 , pp. 669-698
    • Nevai, P.1
  • 25
    • 0006032858 scopus 로고
    • An algorithm for the numerical evaluation of certain Cauchy principal value integrals
    • D. F. Paget and D. Elliott, An algorithm for the numerical evaluation of certain Cauchy principal value integrals, Numer. Math., 19 (1972), pp. 373-385.
    • (1972) Numer. Math. , vol.19 , pp. 373-385
    • Paget, D.F.1    Elliott, D.2
  • 26
    • 0041699072 scopus 로고
    • Modified Clenshaw-Curtis integration and applications to numerical computation of integral transforms
    • Numerical Integration, Recent Developments, Software and Applications, P. Keast and G. Fairweather (eds.), D. Reidel Publishing Company
    • R. Piessens, Modified Clenshaw-Curtis integration and applications to numerical computation of integral transforms, in Numerical Integration, Recent Developments, Software and Applications, NATO ASI Series, vol. 203, P. Keast and G. Fairweather (eds.), D. Reidel Publishing Company, (1987), pp. 35-51.
    • (1987) NATO ASI Series , vol.203 , pp. 35-51
    • Piessens, R.1
  • 27
    • 0001288628 scopus 로고
    • Numerical solution of integral equations of mathematical physics using Chebyshev polynomials
    • R. Piessens and M. Branders, Numerical solution of integral equations of mathematical physics using Chebyshev polynomials, J. Comput. Phys., 21 (1976), pp. 178-196.
    • (1976) J. Comput. Phys. , vol.21 , pp. 178-196
    • Piessens, R.1    Branders, M.2
  • 28
    • 0040061094 scopus 로고
    • On the convergence and divergence of Hunter's method for Cauchy principal value integrals
    • A. Gerasoulis and R. Vichnevetsky eds., IMACS, New Brunswick, NJ
    • P. Rabinowitz, On the convergence and divergence of Hunter's method for Cauchy principal value integrals, in Numerical Solution of Singular Integral Equation, A. Gerasoulis and R. Vichnevetsky eds., IMACS, 1984, New Brunswick, NJ, pp. 86-88.
    • (1984) Numerical Solution of Singular Integral Equation , pp. 86-88
    • Rabinowitz, P.1
  • 29
    • 0347130405 scopus 로고
    • Bemerkungen zu den Approximationssätzen von Jackson und Jackson-Timan
    • Abstract Spaces and Approximation, P. L. Butzer and B. Szokefalvi-Nagy, eds., Birkhäuser, Basel
    • P. O. Runck, Bemerkungen zu den Approximationssätzen von Jackson und Jackson-Timan, in Abstract Spaces and Approximation, P. L. Butzer and B. Szokefalvi-Nagy, eds., Internationale Schriftenreihe zur Numerischen Mathematik, vol. 10, Birkhäuser, Basel, 1969, pp. 303-308.
    • (1969) Internationale Schriftenreihe Zur Numerischen Mathematik , vol.10 , pp. 303-308
    • Runck, P.O.1
  • 30
    • 0345869170 scopus 로고
    • On the convergence of quadrature process for a singular integral
    • M. A. Sheshko, On the convergence of quadrature process for a singular integral, Soviet. Math. (Iz. VUZ), 20:12 (1976), pp. 86-94.
    • (1976) Soviet. Math. (Iz. VUZ) , vol.20 , Issue.12 , pp. 86-94
    • Sheshko, M.A.1
  • 31
    • 84966227879 scopus 로고
    • On the convergence of a quadrature process for a singular integral with power-logarithmic singularity, Soviet
    • M. A. Sheshko and T. S. Yakimenko, On the convergence of a quadrature process for a singular integral with power-logarithmic singularity, Soviet. Math. (Iz. VUZ), 24:1 (1980), pp. 109-111.
    • (1980) Math. (Iz. VUZ) , vol.24 , Issue.1 , pp. 109-111
    • Sheshko, M.A.1    Yakimenko, T.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.