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Volumn 68, Issue 228, 1999, Pages 1533-1567

Composite wavelet bases for operator equations

Author keywords

Biorthogonal wavelets; Boundary element methods; Composite multiresolution; Multiscale methods for partial differential equations; Norm equivalences

Indexed keywords


EID: 0033426280     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0025-5718-99-01092-3     Document Type: Article
Times cited : (128)

References (47)
  • 2
    • 0040891790 scopus 로고    scopus 로고
    • R.A. Adams, Sobolev Spaces, Academic Press, 1975. MR 56:9247
    • MR , vol.56 , pp. 9247
  • 3
    • 84990610636 scopus 로고    scopus 로고
    • The fast wavelet transform and numerical algorithms
    • G. Beylkin, R. Coifman and V. Rokhlin, The fast wavelet transform and numerical algorithms, Comm. Pure Appl. Math. 44, 1991, 141-183. MR 92c:65061
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 4
    • 84990610636 scopus 로고    scopus 로고
    • G. Beylkin, R. Coifman and V. Rokhlin, The fast wavelet transform and numerical algorithms, Comm. Pure Appl. Math. 44, 1991, 141-183. MR 92c:65061
    • MR , vol.92 C , pp. 65061
  • 6
    • 0040378607 scopus 로고    scopus 로고
    • C. de Boor, A Practical Guide to Splines, Springer, 1978. MR 80a:65027
    • MR , vol.80 A , pp. 65027
  • 8
    • 0041151347 scopus 로고    scopus 로고
    • C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer Series in Computational Physics, Springer, 1988. MR 89m:76004
    • MR , vol.89 M , pp. 76004
  • 10
    • 30244488289 scopus 로고    scopus 로고
    • J.M. Carnicer, W. Dahmen and J.M. Peña, Local decomposition of refinable spaces, Appl. Comp. Harm. Anal. 3, 1996, 127-153. MR 97f:42050
    • MR , vol.97 F , pp. 42050
  • 11
    • 0039161299 scopus 로고
    • Multiscale decompositions on bounded domains
    • preprint, to appear
    • A. Cohen, W. Dahmen and R.A. DeVore, Multiscale decompositions on bounded domains, preprint, 1995, to appear in Trans. Amer. Math. Soc.
    • (1995) Trans. Amer. Math. Soc.
    • Cohen, A.1    Dahmen, W.2    DeVore, R.A.3
  • 12
    • 84990623513 scopus 로고    scopus 로고
    • Biorthogonal bases of compactly supported wavelets
    • A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45, 1992, 485-560. MR 93e:42044
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 485-560
    • Cohen, A.1    Daubechies, I.2    Feauveau, J.-C.3
  • 13
    • 84990623513 scopus 로고    scopus 로고
    • A. Cohen, I. Daubechies and J.-C. Feauveau, Biorthogonal bases of compactly supported wavelets, Comm. Pure Appl. Math. 45, 1992, 485-560. MR 93e:42044
    • MR , vol.93 E , pp. 42044
  • 14
    • 0027840161 scopus 로고    scopus 로고
    • Wavelets on the interval and fast wavelet transforms
    • A. Cohen, I. Daubechies and P. Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comp. Harm. Anal. 1, 1993, 54-81. MR 94m:42074
    • (1993) Appl. Comp. Harm. Anal. , vol.1 , pp. 54-81
    • Cohen, A.1    Daubechies, I.2    Vial, P.3
  • 15
    • 0027840161 scopus 로고    scopus 로고
    • A. Cohen, I. Daubechies and P. Vial, Wavelets on the interval and fast wavelet transforms, Appl. Comp. Harm. Anal. 1, 1993, 54-81. MR 94m:42074
    • MR , vol.94 M , pp. 42074
  • 16
    • 0031069391 scopus 로고    scopus 로고
    • Stable multiscale bases and local error estimation for elliptic problems
    • S. Dahlke, W. Dahmen, R. Hochmuth, R. Schneider, Stable multiscale bases and local error estimation for elliptic problems, Applied Numerical Mathematics 23, 1997, 21-47. MR 98a:65075
    • (1997) Applied Numerical Mathematics , vol.23 , pp. 21-47
    • Dahlke, S.1    Dahmen, W.2    Hochmuth, R.3    Schneider, R.4
  • 17
    • 0031069391 scopus 로고    scopus 로고
    • S. Dahlke, W. Dahmen, R. Hochmuth, R. Schneider, Stable multiscale bases and local error estimation for elliptic problems, Applied Numerical Mathematics 23, 1997, 21-47. MR 98a:65075
    • MR , vol.98 A , pp. 65075
  • 18
    • 1842484444 scopus 로고    scopus 로고
    • Stability of multiscale transformations
    • W. Dahmen, Stability of multiscale transformations, J. Fourier Anal. Appl. 2, 1996, 341-361. MR 97i:46133
    • (1996) J. Fourier Anal. Appl. , vol.2 , pp. 341-361
    • Dahmen, W.1
  • 19
    • 1842484444 scopus 로고    scopus 로고
    • W. Dahmen, Stability of multiscale transformations, J. Fourier Anal. Appl. 2, 1996, 341-361. MR 97i:46133
    • MR , vol.97 I , pp. 46133
  • 20
    • 0003081073 scopus 로고
    • Multiscale analysis, approximation, and interpolation spaces
    • C.K. Chui, L.L. Schumaker (eds.), World Scientific Publishing Co.
    • W. Dahmen, Multiscale analysis, approximation, and interpolation spaces, in: Approximation Theory VIII, C.K. Chui, L.L. Schumaker (eds.), World Scientific Publishing Co., 1995, 47-88. MR 98f:41032
    • (1995) Approximation Theory VIII , pp. 47-88
    • Dahmen, W.1
  • 21
    • 0039381191 scopus 로고    scopus 로고
    • W. Dahmen, Multiscale analysis, approximation, and interpolation spaces, in: Approximation Theory VIII, C.K. Chui, L.L. Schumaker (eds.), World Scientific Publishing Co., 1995, 47-88. MR 98f:41032
    • MR , vol.98 F , pp. 41032
  • 22
    • 85011480386 scopus 로고    scopus 로고
    • Wavelet and multiscale methods for operator equations
    • Cambridge University Press
    • W. Dahmen, Wavelet and multiscale methods for operator equations, Cambridge University Press, Acta Numerica 6, 1997, 55-228. MR 98m:65102
    • (1997) Acta Numerica , vol.6 , pp. 55-228
    • Dahmen, W.1
  • 23
    • 85011480386 scopus 로고    scopus 로고
    • W. Dahmen, Wavelet and multiscale methods for operator equations, Cambridge University Press, Acta Numerica 6, 1997, 55-228. MR 98m:65102
    • MR , vol.98 M , pp. 65102
  • 24
    • 33845592412 scopus 로고    scopus 로고
    • Multilevel preconditioning
    • W. Dahmen, A. Kunoth, Multilevel preconditioning, Numer. Math. 63, 1992, 315-344. MR 93j:65065
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 25
    • 33845592412 scopus 로고    scopus 로고
    • W. Dahmen, A. Kunoth, Multilevel preconditioning, Numer. Math. 63, 1992, 315-344. MR 93j:65065
    • MR , vol.93 J , pp. 65065
  • 26
    • 0007152988 scopus 로고    scopus 로고
    • Biorthogonal spline-wavelets on the interval - Stability and moment conditions
    • IGPM Report # 129, RWTH Aachen, to appear
    • W. Dahmen, A. Kunoth and K. Urban, Biorthogonal spline-wavelets on the interval - Stability and moment conditions, IGPM Report # 129, RWTH Aachen, 1996, to appear in Appl. Computational Harm. Anal.
    • (1996) Appl. Computational Harm. Anal.
    • Dahmen, W.1    Kunoth, A.2    Urban, K.3
  • 27
    • 51249161722 scopus 로고    scopus 로고
    • Wavelet approximation methods for periodic pseudodifferential equations. Part 1 - Convergence analysis
    • W. Dahmen, S. Prößdorf, R. Schneider, Wavelet approximation methods for periodic pseudodifferential equations. Part 1 - Convergence analysis, Math. Zeitschrift 215, 1994, 583-620. MR 95g:65148
    • (1994) Math. Zeitschrift , vol.215 , pp. 583-620
    • Dahmen, W.1    Prößdorf, S.2    Schneider, R.3
  • 28
    • 51249161722 scopus 로고    scopus 로고
    • W. Dahmen, S. Prößdorf, R. Schneider, Wavelet approximation methods for periodic pseudodifferential equations. Part 1 - Convergence analysis, Math. Zeitschrift 215, 1994, 583-620. MR 95g:65148
    • MR , vol.95 G , pp. 65148
  • 29
    • 0000827236 scopus 로고    scopus 로고
    • Wavelet approximation methods for periodic pseudodifferential equations. Part 2 - Fast solution and matrix compression
    • W. Dahmen, S. Prößdorf, R. Schneider, Wavelet approximation methods for periodic pseudodifferential equations. Part 2 - Fast solution and matrix compression, Advances in Computational Mathematics 1, 1993, 259-335. MR 95g:65149
    • (1993) Advances in Computational Mathematics , vol.1 , pp. 259-335
    • Dahmen, W.1    Prößdorf, S.2    Schneider, R.3
  • 30
    • 0000827236 scopus 로고    scopus 로고
    • W. Dahmen, S. Prößdorf, R. Schneider, Wavelet approximation methods for periodic pseudodifferential equations. Part 2 - Fast solution and matrix compression, Advances in Computational Mathematics 1, 1993, 259-335. MR 95g:65149
    • MR , vol.95 G , pp. 65149
  • 32
    • 85011468924 scopus 로고    scopus 로고
    • W. Dahmen, S. Prößdorf, R. Schneider, Multiscale methods for pseudo-differential equations on smooth manifolds, in: Proceedings of the International Conference on Wavelets: Theory, Algorithms, and Applications, C.K. Chui, L. Montefusco, L. Puccio (eds.), Academic Press, 1994, 385-424. MR 96c:65208
    • MR , vol.96 C , pp. 65208
  • 33
    • 0000619262 scopus 로고    scopus 로고
    • Wavelet bases with complementary boundary conditions - Function spaces on the cube
    • W. Dahmen, R. Schneider, Wavelet bases with complementary boundary conditions - Function spaces on the cube, Results in Mathematics, 34, 1998, 255-293.
    • (1998) Results in Mathematics , vol.34 , pp. 255-293
    • Dahmen, W.1    Schneider, R.2
  • 35
    • 25544448524 scopus 로고    scopus 로고
    • R. Dautray, J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 4, Integral Equations and Numerical Methods, Springer, 1990. MR 91h:00004b
    • MR , vol.91 H
  • 37
    • 0025438485 scopus 로고    scopus 로고
    • K. Höllig and H. Mögerle, G-splines, Comp. Aided Geom. Design 7, 1990, 197-207. MR 91e:65006
    • MR , vol.91 E , pp. 65006
  • 38
    • 0026909957 scopus 로고    scopus 로고
    • Wavelet methods for fast solution of elliptic problems
    • S. Jaffard, Wavelet methods for fast solution of elliptic problems, SIAM J. Numer. Anal. 29, 1992, 965-987. MR 93j:35042
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 965-987
    • Jaffard, S.1
  • 39
    • 0026909957 scopus 로고    scopus 로고
    • S. Jaffard, Wavelet methods for fast solution of elliptic problems, SIAM J. Numer. Anal. 29, 1992, 965-987. MR 93j:35042
    • MR , vol.93 J , pp. 35042
  • 41
    • 0030496223 scopus 로고    scopus 로고
    • Wavelet approximations of the first kind integral equation on plygons
    • T. von Petersdorff and C. Schwab, Wavelet approximations of the first kind integral equation on plygons , Numer. Mathematik 74, 1996, 479-516. MR 97m:65223
    • (1996) Numer. Mathematik , vol.74 , pp. 479-516
    • Von Petersdorff, T.1    Schwab, C.2
  • 42
    • 0030496223 scopus 로고    scopus 로고
    • T. von Petersdorff and C. Schwab, Wavelet approximations of the first kind integral equation on plygons , Numer. Mathematik 74, 1996, 479-516. MR 97m:65223
    • MR , vol.97 M , pp. 65223
  • 43
    • 0029270891 scopus 로고    scopus 로고
    • Biquadratic G-spline surfaces
    • U. Reif, Biquadratic G-spline surfaces, CAGD 12, 1995, 193-205. MR 95k:65022
    • (1995) CAGD , vol.12 , pp. 193-205
    • Reif, U.1
  • 44
    • 0029270891 scopus 로고    scopus 로고
    • U. Reif, Biquadratic G-spline surfaces, CAGD 12, 1995, 193-205. MR 95k:65022
    • MR , vol.95 K , pp. 65022
  • 46
    • 30244489068 scopus 로고    scopus 로고
    • The lifting scheme: A custom-design construction of biorthogonal wavelets
    • W. Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets, Appl. Comput. Harmon. Anal. 3, 1996, 186-200. MR 97b:42060
    • (1996) Appl. Comput. Harmon. Anal. , vol.3 , pp. 186-200
    • Sweldens, W.1
  • 47
    • 30244489068 scopus 로고    scopus 로고
    • W. Sweldens, The lifting scheme: A custom-design construction of biorthogonal wavelets, Appl. Comput. Harmon. Anal. 3, 1996, 186-200. MR 97b:42060
    • MR , vol.97 B , pp. 42060


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