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Volumn 6, Issue 3, 2007, Pages 643-666

Fast numerical collocation solutions of integral equations

Author keywords

Fast multiscale collocation methods; Fredholm integral equations of the second kind; Multilevel augmentation methods

Indexed keywords


EID: 34547927029     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2007.6.643     Document Type: Conference Paper
Times cited : (17)

References (24)
  • 1
    • 25444442673 scopus 로고
    • Numerical solution of Fredholm integral equation of the second kind
    • K.E. Atkinson, Numerical solution of Fredholm integral equation of the second kind, SIAM J. Numer. Anal., 4 (1967), 337-348.
    • (1967) SIAM J. Numer. Anal , vol.4 , pp. 337-348
    • Atkinson, K.E.1
  • 3
    • 22844454627 scopus 로고    scopus 로고
    • A fast matrix-vector multiplication method for solving the radiosity equation
    • K.E. Atkinson and D. Chien, A fast matrix-vector multiplication method for solving the radiosity equation, Adv. Comput. Math., 12 (2000), 151-174.
    • (2000) Adv. Comput. Math , vol.12 , pp. 151-174
    • Atkinson, K.E.1    Chien, D.2
  • 4
    • 0000416592 scopus 로고    scopus 로고
    • The collocation method for solving the radiosity equation for unoccluded surfaces
    • K.E. Atkinson and G. Chandler, The collocation method for solving the radiosity equation for unoccluded surfaces, J. Integral Equations Appl., 10 (1998), 253-290.
    • (1998) J. Integral Equations Appl , vol.10 , pp. 253-290
    • Atkinson, K.E.1    Chandler, G.2
  • 5
    • 0009286111 scopus 로고
    • Piecewise continuous collocation for integral equations
    • K.E. Atkinson, I. Graham and I. Sloan, Piecewise continuous collocation for integral equations, SIAM J. Numer. Anal., 20 (1983), 172-186.
    • (1983) SIAM J. Numer. Anal , vol.20 , pp. 172-186
    • Atkinson, K.E.1    Graham, I.2    Sloan, I.3
  • 6
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms I
    • G. Beylkin, R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), 141-183.
    • (1991) Comm. Pure Appl. Math , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 7
    • 21744452540 scopus 로고    scopus 로고
    • The Petrov-Galerkin methods for second kind integral equations II: Multiwavelet scheme
    • Z. Chen, C.A. Micchelli and Y. Xu, The Petrov-Galerkin methods for second kind integral equations II: Multiwavelet scheme, Adv. Comp. Math., 7 (1997), 199-233.
    • (1997) Adv. Comp. Math , vol.7 , pp. 199-233
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 8
    • 0033456757 scopus 로고    scopus 로고
    • A construction of interpolating wavelets on invariant sets
    • Z. Chen, C.A. Micchelli and Y. Xu, A construction of interpolating wavelets on invariant sets, Math. Comp., 68 (1999), 1560-1587.
    • (1999) Math. Comp , vol.68 , pp. 1560-1587
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 9
    • 0035888656 scopus 로고    scopus 로고
    • A multilevel method for solving operator equations
    • Z. Chen, C.A. Micchelli and Y. Xu, A multilevel method for solving operator equations, J. Math. Anal. Appl., 262 (2001), 688-699.
    • (2001) J. Math. Anal. Appl , vol.262 , pp. 688-699
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 10
    • 0036108418 scopus 로고    scopus 로고
    • Discrete wavelet Petrov-Galerkin methods
    • Z. Chen, C.A. Micchelli and Y. Xu, Discrete wavelet Petrov-Galerkin methods, Adv. Comp. Math., 16 (2002), 1-28.
    • (2002) Adv. Comp. Math , vol.16 , pp. 1-28
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 11
    • 0036556665 scopus 로고    scopus 로고
    • Fast collocation methods for second kind integral equations
    • Z. Chen, C.A. Micchelli and Y. Xu, Fast collocation methods for second kind integral equations, SIAM J. Numer. Anal., 40 (2002), 344-375.
    • (2002) SIAM J. Numer. Anal , vol.40 , pp. 344-375
    • Chen, Z.1    Micchelli, C.A.2    Xu, Y.3
  • 12
  • 13
    • 0005554354 scopus 로고
    • A multiscale method for the double layer potential equation on a polyhedron
    • Advances in computational mathematics New Delhi, World Sci. Publishing, River Edge, NJ
    • W. Dahmen, B. Kleemann, S. Proessdorf and R. Schneider, A multiscale method for the double layer potential equation on a polyhedron, in "Advances in computational mathematics" (New Delhi, 1993), 15-57, Ser. Approx. Decompos., 4, World Sci. Publishing, River Edge, NJ, 1994.
    • (1993) Ser. Approx. Decompos , vol.4 , pp. 15-57
    • Dahmen, W.1    Kleemann, B.2    Proessdorf, S.3    Schneider, R.4
  • 14
    • 51249161722 scopus 로고
    • Wavelet approximation methods for pseudodifferential equations I. Stability and convergence
    • W. Dahmen, S. Proessdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations I. Stability and convergence, Math. Z., 215 (1994), 583-620.
    • (1994) Math. Z , vol.215 , pp. 583-620
    • Dahmen, W.1    Proessdorf, S.2    Schneider, R.3
  • 15
    • 0000827236 scopus 로고
    • Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solutions
    • W. Dahmen, S. Proessdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solutions. Adv. Comput. Math., 1 (1993), 259-335.
    • (1993) Adv. Comput. Math , vol.1 , pp. 259-335
    • Dahmen, W.1    Proessdorf, S.2    Schneider, R.3
  • 16
    • 1842823646 scopus 로고    scopus 로고
    • An implementation of fast wavelet Galerkin methods for integral equations of the second kind
    • W. Fang, Y. Wang and Y. Xu, An implementation of fast wavelet Galerkin methods for integral equations of the second kind, J. Scientific Computing, 20 (2004), 277-302.
    • (2004) J. Scientific Computing , vol.20 , pp. 277-302
    • Fang, W.1    Wang, Y.2    Xu, Y.3
  • 17
    • 0001265433 scopus 로고
    • Fractals and self similarity
    • J.E. Hutchinson, Fractals and self similarity, Indiana Univ. Math. J., 30 (1981), 713-747.
    • (1981) Indiana Univ. Math. J , vol.30 , pp. 713-747
    • Hutchinson, J.E.1
  • 18
    • 0141514730 scopus 로고    scopus 로고
    • Wavelet collocation methods for a first kind boundary integral equation in acoustic scattering
    • G.C. Hsiao and A. Rathsfeld, Wavelet collocation methods for a first kind boundary integral equation in acoustic scattering, Adv. Comput. Math., 17 (2002), 281-308.
    • (2002) Adv. Comput. Math , vol.17 , pp. 281-308
    • Hsiao, G.C.1    Rathsfeld, A.2
  • 19
    • 0028499152 scopus 로고
    • Using the matrix refinement equation for the construction of wavelets on invariant sets
    • C.A. Micchelli and Y. Xu, Using the matrix refinement equation for the construction of wavelets on invariant sets, Appl. Comput. Harmon. Anal., 1 (1994), 391-401.
    • (1994) Appl. Comput. Harmon. Anal , vol.1 , pp. 391-401
    • Micchelli, C.A.1    Xu, Y.2
  • 20
    • 0031277073 scopus 로고    scopus 로고
    • Wavelet Galerkin methods for second-kind integral equations
    • C.A. Micchelli, Y. Xu and Y. Zhao, Wavelet Galerkin methods for second-kind integral equations, J. Comput. Appl. Math., 86 (1997), 251-270.
    • (1997) J. Comput. Appl. Math , vol.86 , pp. 251-270
    • Micchelli, C.A.1    Xu, Y.2    Zhao, Y.3
  • 21
    • 0030496223 scopus 로고    scopus 로고
    • Wavelet approximation of first kind integral equations in a polygon
    • T. von Petersdorff and C Schwab, Wavelet approximation of first kind integral equations in a polygon, Numer. Math., 74 (1996), 479-516.
    • (1996) Numer. Math , vol.74 , pp. 479-516
    • von Petersdorff, T.1    Schwab, C.2
  • 23
    • 0041815525 scopus 로고    scopus 로고
    • A. Rathsfeld, A wavelet algorithm for the solution of a singular integral equation over a smooth two-dimensional manifold, J. Integral Equations Appl., 10 (1998), 445-501.
    • A. Rathsfeld, A wavelet algorithm for the solution of a singular integral equation over a smooth two-dimensional manifold, J. Integral Equations Appl., 10 (1998), 445-501.
  • 24
    • 34547948511 scopus 로고    scopus 로고
    • R. Schneider, Multiskalen- und wavelet-Matrixkompression: Analyiss-sasierte Methoden zur effizienten Lösung großer vollbesetzter Gleichungs-systeme, Habilitationsschrift, Technische Hochschule Darmstadt, 1995.
    • R. Schneider, "Multiskalen- und wavelet-Matrixkompression: Analyiss-sasierte Methoden zur effizienten Lösung großer vollbesetzter Gleichungs-systeme," Habilitationsschrift, Technische Hochschule Darmstadt, 1995.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.