메뉴 건너뛰기




Volumn 78, Issue 2, 1997, Pages 255-275

A new algorithm for Cauchy principal value and Hadamard finite-part integrals

Author keywords

Convergence; Finite part integrals; Orthogonal polynomials; Quadrature rules

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; INTEGRAL EQUATIONS; POLYNOMIALS;

EID: 0031076042     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(96)00142-2     Document Type: Article
Times cited : (47)

References (28)
  • 1
    • 0040332408 scopus 로고
    • A sinc quadrature rule for Hadamard finite-part integrals
    • B. Bialecki, A Sinc quadrature rule for Hadamard finite-part integrals, Numer. Math. 57 (1990) 263-269.
    • (1990) Numer. Math. , vol.57 , pp. 263-269
    • Bialecki, B.1
  • 2
    • 0038909406 scopus 로고
    • Complex Gauss-Kronrod integration rules for certain Cauchy principal value integrals
    • F. Caliò and E. Marchetti, Complex Gauss-Kronrod integration rules for certain Cauchy principal value integrals, Computing 50 (1993) 165-173.
    • (1993) Computing , vol.50 , pp. 165-173
    • Caliò, F.1    Marchetti, E.2
  • 3
    • 0023843896 scopus 로고
    • On the convergence of a rule by Monegato for the numerical evaluation of Cauchy principal value integrals
    • C. Chiodo and G. Criscuolo, On the convergence of a rule by Monegato for the numerical evaluation of Cauchy principal value integrals, Computing 40 (1988) 67-74.
    • (1988) Computing , vol.40 , pp. 67-74
    • Chiodo, C.1    Criscuolo, G.2
  • 4
    • 0041318484 scopus 로고
    • On the uniform convergence of modified gaussian rules for the numerical evaluation of derivatives of principal value integrals
    • G. Milovanovic, Ed., Nis/Yugosl. (1987) Univ. Niš
    • G. Criscuolo and G. Mastroianni, On the uniform convergence of modified Gaussian rules for the numerical evaluation of derivatives of principal value integrals, in: G. Milovanovic, Ed., Numerical Methods and Approximation Theory III 3rd Conf., Nis/Yugosl. (1987) (Univ. Niš, 1988) 139-147.
    • (1988) Numerical Methods and Approximation Theory III 3rd Conf. , pp. 139-147
    • Criscuolo, G.1    Mastroianni, G.2
  • 5
    • 0000357289 scopus 로고
    • On the convergence of product formulas for the numerical evaluation of derivatives of Cauchy principal value integrals
    • G. Criscuolo and 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) 713-727.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 713-727
    • Criscuolo, G.1    Mastroianni, G.2
  • 6
    • 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) 445-461.
    • (1989) Numer. Math. , vol.54 , pp. 445-461
    • Criscuolo, G.1    Mastroianni, G.2
  • 7
    • 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 Approx. Theory - A Special Volume of J. Approx. Theory (Academic Press, New York, 1991) 141-176.
    • (1991) Progress in Approx. Theory - A Special Volume of J. Approx. Theory , pp. 141-176
    • Criscuolo, G.1    Mastroianni, G.2
  • 8
    • 0002606438 scopus 로고
    • Finite-part integrals: Their occurence and computation
    • F. Altomare and G. Mastroianni, Eds., Proc. 2nd Internat. Conf. in Functional Analysis and Approximation Theory, (1993) Circ. Matem. Palermo Soc.
    • M. Diligenti and G. Monegato, Finite-part integrals: their occurence and computation, in: F. Altomare and G. Mastroianni, Eds., Proc. 2nd Internat. Conf. in Functional Analysis and Approximation Theory, Suppl. Rend. Circ. Matem. Palermo Ser. II 33 (1993) (Circ. Matem. Palermo Soc., 1993) 39-61.
    • (1993) Suppl. Rend. Circ. Matem. Palermo Ser. II , vol.33 , pp. 39-61
    • Diligenti, M.1    Monegato, G.2
  • 9
    • 21344497166 scopus 로고
    • An asymptotic analysis of two-algorithms for certain Hadamard finite-part integrals
    • D. Elliott, An asymptotic analysis of two-algorithms for certain Hadamard finite-part integrals, IMA J. Numer. Anal. 13 (1993) 445-462.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 445-462
    • Elliott, D.1
  • 10
    • 0028427025 scopus 로고
    • Hilbert and Hadamard transforms by generalized Chebyshev expansions
    • T. Hagasawa and T. Torii, Hilbert and Hadamard transforms by generalized Chebyshev expansions, J. Comput. Appl. Math. 51 (1994) 71-83.
    • (1994) J. Comput. Appl. Math. , vol.51 , pp. 71-83
    • Hagasawa, T.1    Torii, T.2
  • 11
    • 0002294867 scopus 로고
    • Application of finite-part integrals to the singular integral equation of crack problems in plane and three-dimensional elasticity
    • N.I. Ioakimidis, Application of finite-part integrals to the singular integral equation of crack problems in plane and three-dimensional elasticity, Acta Mech. 45 (1982) 31-47.
    • (1982) Acta Mech. , vol.45 , pp. 31-47
    • Ioakimidis, N.I.1
  • 12
    • 84966222583 scopus 로고
    • On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives
    • N.I. Ioakimidis, On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives, Math. Comput. 44 (1985) 191-198.
    • (1985) Math. Comput. , vol.44 , pp. 191-198
    • Ioakimidis, N.I.1
  • 13
    • 0040753061 scopus 로고
    • On the numerical solution of singular integrodifferential equations
    • N.I. Ioakimidis and P.S. Theocaris, On the numerical solution of singular integrodifferential equations, Quart. Appl. Math. 37 (1979) 325-331.
    • (1979) Quart. Appl. Math. , vol.37 , pp. 325-331
    • Ioakimidis, N.I.1    Theocaris, P.S.2
  • 14
    • 0001863547 scopus 로고
    • On the solution of integral equations with strongly singular kernels
    • A.C. Kaya and F. Erdogan, On the solution of integral equations with strongly singular kernels, Quart. Appl. Math. 45 (1987) 105-122.
    • (1987) Quart. Appl. Math. , vol.45 , pp. 105-122
    • Kaya, A.C.1    Erdogan, F.2
  • 15
    • 0000249956 scopus 로고
    • The numerical evaluation of principal value integrals by finite-part integration
    • H.R. Kutt, The numerical evaluation of principal value integrals by finite-part integration, Numer. Math. 24 (1975) 205-210.
    • (1975) Numer. Math. , vol.24 , pp. 205-210
    • Kutt, H.R.1
  • 16
    • 0022197247 scopus 로고
    • On the approximate computation of certain strongly singular integrals
    • P. Linz, On the approximate computation of certain strongly singular integrals, Computing 35 (1985) 345-353.
    • (1985) Computing , vol.35 , pp. 345-353
    • Linz, P.1
  • 17
    • 0041819132 scopus 로고
    • Evaluation of the acoustic impedance of a screen
    • C. Macaskill and E.O. Tuck, Evaluation of the acoustic impedance of a screen, J. Austral. Math. Soc. Ser. B 20 (1977) 46-61.
    • (1977) J. Austral. Math. Soc. Ser. B , vol.20 , pp. 46-61
    • Macaskill, C.1    Tuck, E.O.2
  • 18
    • 0003774712 scopus 로고
    • Uniform convergence of derivatives of Lagrange interpolation
    • G. Mastroianni, Uniform convergence of derivatives of Lagrange interpolation, J. Comput. Appl. Math. 43 (1992) 37-51.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 37-51
    • Mastroianni, G.1
  • 19
    • 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) 337-354.
    • (1982) Computing , vol.29 , pp. 337-354
    • Monegato, G.1
  • 20
    • 34250104499 scopus 로고
    • On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives
    • G. Monegato, On the weights of certain quadratures for the numerical evaluation of Cauchy principal value integrals and their derivatives, Numer. Math. 50 (1987) 273-281.
    • (1987) Numer. Math. , vol.50 , pp. 273-281
    • Monegato, G.1
  • 21
    • 0028422932 scopus 로고
    • Numerical evaluation of hypersingular integrals
    • G. Monegato, Numerical evaluation of hypersingular integrals, J. Comput. Appl. Math. 50 (1994) 9-31.
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 9-31
    • Monegato, G.1
  • 22
    • 0000956929 scopus 로고
    • Orthogonal polynomials
    • Amer. Math. Soc., Providence, RI
    • P. Nevai, Orthogonal Polynomials, Mem. Amer. Math. Soc., Vol. 213 (Amer. Math. Soc., Providence, RI, 1979).
    • (1979) Mem. Amer. Math. Soc. , vol.213
    • Nevai, P.1
  • 23
    • 0010678017 scopus 로고
    • Generalized functions and divergent integrals
    • B.W. Ninham, Generalized functions and divergent integrals, Numer. Math. 8 (1966) 444-457.
    • (1966) Numer. Math. , vol.8 , pp. 444-457
    • Ninham, B.W.1
  • 24
    • 0001323697 scopus 로고
    • A quadrature rule for finite-part integrals
    • D.F. Paget, A quadrature rule for finite-part integrals, BIT 21 (1981) 212-220.
    • (1981) BIT , vol.21 , pp. 212-220
    • Paget, D.F.1
  • 25
    • 0001643631 scopus 로고
    • The numerical evaluation of Hadamard finite-part integrals
    • D.F. Paget, The numerical evaluation of Hadamard finite-part integrals, Numer. Math. 36 (1981) 447-453.
    • (1981) Numer. Math. , vol.36 , pp. 447-453
    • Paget, D.F.1
  • 26
    • 0041819130 scopus 로고
    • Calculating singular integrals as an ill-posed problem
    • A.G. Ramm and A. van der Sluis, Calculating singular integrals as an ill-posed problem, Numer. Math. 57 (1990) 139-145.
    • (1990) Numer. Math. , vol.57 , pp. 139-145
    • Ramm, A.G.1    Van Der Sluis, A.2
  • 27
    • 0004073954 scopus 로고
    • Orthogonal polynomials
    • Amer. Math. Soc., Providence, RI
    • G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., Vol. 23 (Amer. Math. Soc., Providence, RI, 1967).
    • (1967) Amer. Math. Soc. Colloq. Publ. , vol.23
    • Szegö, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.