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Volumn 44, Issue 4, 2006, Pages 1351-1374

Projection methods and condition numbers in uniform norm for Fredholm and Cauchy singular integral equations

Author keywords

Cauchy singular integral equation; Fourier sum; Fredholm integral equations; Lagrange interpolation; Projection method

Indexed keywords

APPROXIMATION THEORY; FOURIER ANALYSIS; INTERPOLATION; NUMERICAL METHODS;

EID: 34547944042     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050626934     Document Type: Article
Times cited : (29)

References (51)
  • 2
    • 34547941759 scopus 로고    scopus 로고
    • B. BIALECKI, Sinc quadratures for Cauchy principal value integrals, in Numerical Integration (Bergen, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 357, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992, pp. 81-92.
    • B. BIALECKI, Sinc quadratures for Cauchy principal value integrals, in Numerical Integration (Bergen, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 357, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1992, pp. 81-92.
  • 4
    • 0039531945 scopus 로고    scopus 로고
    • Uniform convergence estimates for a collocation method for the Cauchy singular integral equation
    • M. R. CAPOBIANCO AND M. G. RUSSO, Uniform convergence estimates for a collocation method for the Cauchy singular integral equation, J. Integral Equations Appl., 9 (1997), pp. 21-45.
    • (1997) J. Integral Equations Appl , vol.9 , pp. 21-45
    • CAPOBIANCO, M.R.1    RUSSO, M.G.2
  • 5
    • 0002141721 scopus 로고
    • On the convergence of the Gauss quadrature rules for the Cauchy principal value integrals
    • G. CRISCUOLO AND G. MASTROIANNI, On the convergence of the Gauss quadrature rules for the Cauchy principal value integrals, Ricerche Mat., 3 (1986), pp. 45-60.
    • (1986) Ricerche Mat , vol.3 , pp. 45-60
    • CRISCUOLO, G.1    MASTROIANNI, G.2
  • 6
    • 0023249202 scopus 로고
    • On the convergence of product formulas for the evaluation of certain two-dimensional Cauchy principal value integrals
    • G. CRISCUOLO AND G. MASTROIANNI, On the convergence of product formulas for the evaluation of certain two-dimensional Cauchy principal value integrals, BIT, 27 (1987), pp. 72-84.
    • (1987) BIT , vol.27 , pp. 72-84
    • CRISCUOLO, G.1    MASTROIANNI, G.2
  • 7
    • 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
  • 8
    • 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. 445-461.
    • (1989) Numer. Math , vol.54 , pp. 445-461
    • CRISCUOLO, G.1    MASTROIANNI, G.2
  • 9
    • 34547948526 scopus 로고    scopus 로고
    • Mapping properties of some singular operators in Besov type subspaces of C(-1, 1)
    • to appear
    • M. C. DE BONIS AND G. MASTROIANNI, Mapping properties of some singular operators in Besov type subspaces of C(-1, 1), Integral Equations Operator Theory, to appear.
    • Integral Equations Operator Theory
    • DE BONIS, M.C.1    MASTROIANNI, G.2
  • 11
    • 84968511055 scopus 로고
    • Remarks on Besov spaces and best polynomial approximation
    • Z. DITZIAN AND V. TOTIK, Remarks on Besov spaces and best polynomial approximation, Proc. Amer. Math. Soc., 104 (1988), pp. 1059-1066.
    • (1988) Proc. Amer. Math. Soc , vol.104 , pp. 1059-1066
    • DITZIAN, Z.1    TOTIK, V.2
  • 14
    • 0030834914 scopus 로고    scopus 로고
    • Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution
    • P. JUNGHANNS AND U. LUTHER, Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution, J. Comput. Appl. Math., 77 (1997), pp. 201-237.
    • (1997) J. Comput. Appl. Math , vol.77 , pp. 201-237
    • JUNGHANNS, P.1    LUTHER, U.2
  • 15
    • 34547949867 scopus 로고    scopus 로고
    • P. JUNGHANNS AND U. LUTHER, Uniform convergence of the quadrature method for Cauchy singular integral equations with weakly singular perturbation kernels, in Proceedings of the 3rd International Conference on Functional Analysis and Approximation Theory, II (Acquafredda di Maratea, 1996), Rend. Circ. Mat. Palermo (2) Suppl., 52 (1988), pp. 551-566.
    • P. JUNGHANNS AND U. LUTHER, Uniform convergence of the quadrature method for Cauchy singular integral equations with weakly singular perturbation kernels, in Proceedings of the 3rd International Conference on Functional Analysis and Approximation Theory, Vol. II (Acquafredda di Maratea, 1996), Rend. Circ. Mat. Palermo (2) Suppl., 52 (1988), pp. 551-566.
  • 17
    • 0002690124 scopus 로고
    • Zur Theorie der Näherungsverfahren für singuläre Integralgleichungen auf Intervallen
    • P. JUNGHANNS AND B. SILBERMANN, Zur Theorie der Näherungsverfahren für singuläre Integralgleichungen auf Intervallen, Math. Nachr., 103 (1981), pp. 199-244.
    • (1981) Math. Nachr , vol.103 , pp. 199-244
    • JUNGHANNS, P.1    SILBERMANN, B.2
  • 18
    • 34547933990 scopus 로고    scopus 로고
    • P. JUNGHANNS AND B. SILBERMANN, Numerical Analysis of the Quadrature Method for Solving Linear and Nonlinear Singular Integral Equations, Wiss. Schriftenreihe d. TUK, Germany, 10/1988.
    • P. JUNGHANNS AND B. SILBERMANN, Numerical Analysis of the Quadrature Method for Solving Linear and Nonlinear Singular Integral Equations, Wiss. Schriftenreihe d. TUK, Germany, 10/1988.
  • 20
    • 34547950868 scopus 로고    scopus 로고
    • C. LAURITA AND G. MASTROIANNI, Revisiting a quadrature method for Cauchy singular integral equations with a weakly singular perturbation kernel, in Problems and Methods in Mathematical Physics (Chemnitz, 1999), Oper. Theory Adv. Appl. 121, Birkhäuser, Basel, 2001, pp. 307-326.
    • C. LAURITA AND G. MASTROIANNI, Revisiting a quadrature method for Cauchy singular integral equations with a weakly singular perturbation kernel, in Problems and Methods in Mathematical Physics (Chemnitz, 1999), Oper. Theory Adv. Appl. 121, Birkhäuser, Basel, 2001, pp. 307-326.
  • 21
    • 0141535462 scopus 로고    scopus 로고
    • Condition numbers in numerical methods for Fredholm integral equations of the second kind
    • C. LAURITA AND G. MASTROIANNI, Condition numbers in numerical methods for Fredholm integral equations of the second kind, J. Integral Equations Appl., 14 (2002), pp. 311-341.
    • (2002) J. Integral Equations Appl , vol.14 , pp. 311-341
    • LAURITA, C.1    MASTROIANNI, G.2
  • 23
    • 33749577664 scopus 로고    scopus 로고
    • Problems and Methods in Mathematical Physics Chemnitz, Oper. Theory Adv. Appl. 121, Birkhäuser, Basel
    • ∞ spaces, in Problems and Methods in Mathematical Physics (Chemnitz, 1999), Oper. Theory Adv. Appl. 121, Birkhäuser, Basel, 2001, pp. 327-351.
    • (1999) ∞ spaces , pp. 327-351
    • LUTHER, U.1    MASTROIANNI, G.2
  • 24
    • 0033632575 scopus 로고    scopus 로고
    • Boundedness of the Hilbert transformation in some weighted Besov type spaces
    • U. LUTHER AND M. G. RUSSO, Boundedness of the Hilbert transformation in some weighted Besov type spaces, Integral Equations Operator Theory, 36 (2000), pp. 220-240.
    • (2000) Integral Equations Operator Theory , vol.36 , pp. 220-240
    • LUTHER, U.1    RUSSO, M.G.2
  • 25
    • 0003839152 scopus 로고
    • Some nodes matrices appearing in the numerical analysis for singular integral equations
    • G. MASTROIANNI AND S. PRÖSSDORF, Some nodes matrices appearing in the numerical analysis for singular integral equations, BIT, 34 (1994), pp. 120-128.
    • (1994) BIT , vol.34 , pp. 120-128
    • MASTROIANNI, G.1    PRÖSSDORF, S.2
  • 26
    • 0040224955 scopus 로고
    • A quadrature method for Cauchy integral equations with weakly singular perturbation kernel
    • G. MASTROIANNI AND S. PRÖSSDORF, A quadrature method for Cauchy integral equations with weakly singular perturbation kernel, J. Integral Equations Appl., 4 (1992), pp. 205-228.
    • (1992) J. Integral Equations Appl , vol.4 , pp. 205-228
    • MASTROIANNI, G.1    PRÖSSDORF, S.2
  • 28
    • 0033473442 scopus 로고    scopus 로고
    • Lagrange interpolation in weighted Besov spaces
    • G. MASTROIANNI AND M. G. RUSSO, Lagrange interpolation in weighted Besov spaces, Constr. Approx., 15 (1999), pp. 257-289.
    • (1999) Constr. Approx , vol.15 , pp. 257-289
    • MASTROIANNI, G.1    RUSSO, M.G.2
  • 29
    • 34547900807 scopus 로고    scopus 로고
    • Weighted Marcinkiewicz inequalities and boundedness of the Lagrange operator
    • Hadronic Press, Palm Harbor, FL
    • G. MASTROIANNI AND M. G. RUSSO, Weighted Marcinkiewicz inequalities and boundedness of the Lagrange operator, in Mathematical Analysis and Applications, Hadronic Press, Palm Harbor, FL, 2000, pp. 149-182.
    • (2000) Mathematical Analysis and Applications , pp. 149-182
    • MASTROIANNI, G.1    RUSSO, M.G.2
  • 33
    • 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), pp. 273-281.
    • (1987) Numer. Math , vol.50 , pp. 273-281
    • MONEGATO, G.1
  • 34
    • 0003807469 scopus 로고
    • Product formulas for Fredholm integral equations with rational kernel functions
    • H. Brass and G. Hämerlin, eds, Birkhäuser, Basel
    • G. MONEGATO AND A. PALAMARA ORSI, Product formulas for Fredholm integral equations with rational kernel functions, in Numerical Integration III 85, H. Brass and G. Hämerlin, eds., Birkhäuser, Basel, 1987, pp. 140-156.
    • (1987) Numerical Integration III , vol.85 , pp. 140-156
    • MONEGATO, G.1    PALAMARA ORSI, A.2
  • 35
    • 34547927356 scopus 로고    scopus 로고
    • G. MONEGATO AND S. PRÖSSDORF, Uniform convergence estimates for a collocation and a discrete collocation method for the generalized airfoil equation, in Contributions to Numerical Mathematics, A.G. Argaval, ed., World Scientific, River Edge, NJ, 1993, pp. 285-299 (see also the errata correge in the Internal Reprint No. 14 (1993) Dip. Mat. Politecnico di Torino).
    • G. MONEGATO AND S. PRÖSSDORF, Uniform convergence estimates for a collocation and a discrete collocation method for the generalized airfoil equation, in Contributions to Numerical Mathematics, A.G. Argaval, ed., World Scientific, River Edge, NJ, 1993, pp. 285-299 (see also the errata correge in the Internal Reprint No. 14 (1993) Dip. Mat. Politecnico di Torino).
  • 36
    • 84998260480 scopus 로고
    • An IMT-type double exponential formula for numerical integration
    • M. MORI, An IMT-type double exponential formula for numerical integration, Publ. Res. Inst. Math. Sci., 14 (1978), pp. 713-728.
    • (1978) Publ. Res. Inst. Math. Sci , vol.14 , pp. 713-728
    • MORI, M.1
  • 38
    • 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
  • 39
    • 38249020931 scopus 로고    scopus 로고
    • P. NEVAI, Hilbert transforms and Lagrange interpolation (letter to the editor), J. Approx. Theory, 60 (1990), pp. 360-363.
    • P. NEVAI, Hilbert transforms and Lagrange interpolation (letter to the editor), J. Approx. Theory, 60 (1990), pp. 360-363.
  • 40
    • 38149143213 scopus 로고
    • The double exponential formula for oscillatory functions over the half infinite interval
    • T. OOURA AND M. MORI, The double exponential formula for oscillatory functions over the half infinite interval, J. Comput. Appl. Math., 38 (1991), pp. 353-360.
    • (1991) J. Comput. Appl. Math , vol.38 , pp. 353-360
    • OOURA, T.1    MORI, M.2
  • 42
    • 34547944876 scopus 로고    scopus 로고
    • R. PIESSENS, Modified Clenshaw- Curtis integration and applications to numerical computation of integral transforms, in Numerical Integration (Halifax-N.S., 1986), P. Keast and G. Fairweather, eds., Reidel, Dordrecht, The Netherlands, 1987, pp. 35-51.
    • R. PIESSENS, Modified Clenshaw- Curtis integration and applications to numerical computation of integral transforms, in Numerical Integration (Halifax-N.S., 1986), P. Keast and G. Fairweather, eds., Reidel, Dordrecht, The Netherlands, 1987, pp. 35-51.
  • 43
    • 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
  • 44
    • 0001046705 scopus 로고
    • The mean convergence of orthogonal series II
    • H. POLLARD, The mean convergence of orthogonal series II, Trans. Amer. Math. Soc., 63 (1948), pp. 355-367.
    • (1948) Trans. Amer. Math. Soc , vol.63 , pp. 355-367
    • POLLARD, H.1
  • 46
    • 0001954473 scopus 로고
    • A quadrature-based approach to improving the collocation method
    • I. H. SLOAN, A quadrature-based approach to improving the collocation method, Numer. Math., 54 (1988), pp. 41-56.
    • (1988) Numer. Math , vol.54 , pp. 41-56
    • SLOAN, I.H.1
  • 47
    • 0039271997 scopus 로고
    • Projection methods for integral equation on the half line
    • I. H. SLOAN AND A. SPENCE, Projection methods for integral equation on the half line, IMA J. Numer. Anal., 6 (1986), pp 153-172.
    • (1986) IMA J. Numer. Anal , vol.6 , pp. 153-172
    • SLOAN, I.H.1    SPENCE, A.2
  • 48
    • 0005657127 scopus 로고
    • Superconvergence of the Galerkin iterates for integral equations of the second kind
    • I. H. SLOAN AND V. THOMÉE, Superconvergence of the Galerkin iterates for integral equations of the second kind, J. Integral Equations, 9 (1985), pp. 1-23.
    • (1985) J. Integral Equations , vol.9 , pp. 1-23
    • SLOAN, I.H.1    THOMÉE, V.2
  • 50
    • 84996018880 scopus 로고
    • Double exponential formulas for numerical integration
    • H. TAKAHASI AND M. MORI, Double exponential formulas for numerical integration, Publ. Res. Inst. Math. Sci., 9 (1974), pp. 721-741.
    • (1974) Publ. Res. Inst. Math. Sci , vol.9 , pp. 721-741
    • TAKAHASI, H.1    MORI, M.2


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