메뉴 건너뛰기




Volumn 7, Issue , 2000, Pages 417-711

Wavelet methods in numerical analysis

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33846966749     PISSN: 15708659     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S1570-8659(00)07004-6     Document Type: Review
Times cited : (139)

References (204)
  • 1
    • 0003184789 scopus 로고
    • Multiresolution analysis on unstructured meshes: Application to CFD
    • Morton K.W., and Baines M.J. (Eds), Oxford Science Publications
    • Abgrall R. Multiresolution analysis on unstructured meshes: Application to CFD. In: Morton K.W., and Baines M.J. (Eds). Numerical Methods for Fluid Dynamics V (1995), Oxford Science Publications
    • (1995) Numerical Methods for Fluid Dynamics , vol.V
    • Abgrall, R.1
  • 3
    • 0000139676 scopus 로고
    • 2 for the sparse representation of integral operators
    • 2 for the sparse representation of integral operators. SIAM J. Math. Anal. 24 (1993) 246-262
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 246-262
    • Alpert, B.1
  • 6
    • 0008441151 scopus 로고
    • Hierarchical finite element approaches, error estimates and adaptive refinements
    • Whiteman J.R. (Ed), Academic Press, New York
    • Babushka I., Gago J., Kelly D., and Zienkiewicz O. Hierarchical finite element approaches, error estimates and adaptive refinements. In: Whiteman J.R. (Ed). The Mathematics of Finite Elements and Applications IV (1982), Academic Press, New York
    • (1982) The Mathematics of Finite Elements and Applications , vol.IV
    • Babushka, I.1    Gago, J.2    Kelly, D.3    Zienkiewicz, O.4
  • 7
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • Babushka I., and Rheinboldt W.C. Error estimates for adaptive finite element computations. SIAM J. Numer. Anal. 15 (1978) 736-754
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babushka, I.1    Rheinboldt, W.C.2
  • 9
    • 0000811219 scopus 로고
    • On the convergence of a relaxation method with natural constraints on the elliptic operator
    • Bakhvalov N.S. On the convergence of a relaxation method with natural constraints on the elliptic operator. USSR Comp. Math. and Math. Phys. 6 (1966) 101-135
    • (1966) USSR Comp. Math. and Math. Phys. , vol.6 , pp. 101-135
    • Bakhvalov, N.S.1
  • 10
    • 84966225317 scopus 로고
    • An optimal order process for solving finite element equations
    • Bank R.E., and Dupont T. An optimal order process for solving finite element equations. Math. Comp. 36 (1981) 35-51
    • (1981) Math. Comp. , vol.36 , pp. 35-51
    • Bank, R.E.1    Dupont, T.2
  • 11
    • 0002641609 scopus 로고
    • Refinement algorithms and data structures for regular local mesh refinement
    • (Noth-Holland, Amsterdam). Stepleman R., et al. (Ed), IMACS, Amsterdam
    • (Noth-Holland, Amsterdam). Bank R.E., Sherman A.H., and Weiser A. Refinement algorithms and data structures for regular local mesh refinement. In: Stepleman R., et al. (Ed). Scientific Computing (1983), IMACS, Amsterdam 3-17
    • (1983) Scientific Computing , pp. 3-17
    • Bank, R.E.1    Sherman, A.H.2    Weiser, A.3
  • 12
    • 84966215690 scopus 로고
    • Some a posteriori error estimates for elliptic partial differential equations
    • Bank R.E., and Weiser A. Some a posteriori error estimates for elliptic partial differential equations. Math. Comp. 44 (1985) 283-301
    • (1985) Math. Comp. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 13
    • 0001325515 scopus 로고
    • Approximation and estimation bounds for artificial neural networks
    • Barron A.R. Approximation and estimation bounds for artificial neural networks. Machine Learning 14 (1994) 115-133
    • (1994) Machine Learning , vol.14 , pp. 115-133
    • Barron, A.R.1
  • 16
    • 33845201716 scopus 로고
    • A posteriori error estimates for wavelet Galerkin methods
    • Bertoluzza S. A posteriori error estimates for wavelet Galerkin methods. Appl. Math. Lett. 8 (1995) 1-6
    • (1995) Appl. Math. Lett. , vol.8 , pp. 1-6
    • Bertoluzza, S.1
  • 17
    • 70350311089 scopus 로고
    • Adaptive wavelet collocation for the solution of steady state equation
    • Bertoluzza S. Adaptive wavelet collocation for the solution of steady state equation. SPIE Proc. Wavelet Appl. II (1995) 2491
    • (1995) SPIE Proc. Wavelet Appl. , vol.II , pp. 2491
    • Bertoluzza, S.1
  • 18
    • 37949010323 scopus 로고    scopus 로고
    • An adaptive collocation method based on interpolating wavelets
    • Dahmen W., Kurdila A.J., and Oswald P. (Eds), Academic Press, Berlin
    • Bertoluzza S. An adaptive collocation method based on interpolating wavelets. In: Dahmen W., Kurdila A.J., and Oswald P. (Eds). Multiscale Wavelet Methods for PDE's (1997), Academic Press, Berlin
    • (1997) Multiscale Wavelet Methods for PDE's
    • Bertoluzza, S.1
  • 19
    • 0000102411 scopus 로고    scopus 로고
    • Stabilization by multiscale decompositions
    • Bertoluzza S. Stabilization by multiscale decompositions. Appl. Math. Lett. 6 (1998) 129-134
    • (1998) Appl. Math. Lett. , vol.6 , pp. 129-134
    • Bertoluzza, S.1
  • 20
    • 0039443784 scopus 로고
    • On a family of functions spaces
    • Embedding theorems and applications
    • Besov O.V. On a family of functions spaces. Embedding theorems and applications. Dokl. Akad. Nauk USSR 126 (1959) 1163-1165
    • (1959) Dokl. Akad. Nauk USSR , vol.126 , pp. 1163-1165
    • Besov, O.V.1
  • 21
  • 22
    • 0041981841 scopus 로고    scopus 로고
    • An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations
    • Dahmen W., Kurdila A.J., and Oswald P. (Eds), Academic Press, New York
    • Beylkin G., and Keiser J.M. An adaptive pseudo-wavelet approach for solving nonlinear partial differential equations. In: Dahmen W., Kurdila A.J., and Oswald P. (Eds). Multiscale Wavelet Methods for PDE's (1997), Academic Press, New York
    • (1997) Multiscale Wavelet Methods for PDE's
    • Beylkin, G.1    Keiser, J.M.2
  • 23
    • 0001542801 scopus 로고
    • A multiresolution strategy for numerical homogenization
    • Beylkin G., and Brewster M. A multiresolution strategy for numerical homogenization. Appl. Comp. Harm. Anal. 2 (1995) 327-349
    • (1995) Appl. Comp. Harm. Anal. , vol.2 , pp. 327-349
    • Beylkin, G.1    Brewster, M.2
  • 26
    • 0011555839 scopus 로고
    • The quasi-interpolant as a tool in elementary polynomial spline theory
    • Lorentz G.G. (Ed), Academic Press, Berlin
    • de Boor C. The quasi-interpolant as a tool in elementary polynomial spline theory. In: Lorentz G.G. (Ed). Approximation Theory (1973), Academic Press, Berlin
    • (1973) Approximation Theory
    • de Boor, C.1
  • 27
    • 21344488909 scopus 로고
    • On the construction of multivariate pre-wavelets
    • de Boor C., DeVore R., and Ron A. On the construction of multivariate pre-wavelets. Constr. Approx. 9 (1993) 123-166
    • (1993) Constr. Approx. , vol.9 , pp. 123-166
    • de Boor, C.1    DeVore, R.2    Ron, A.3
  • 29
    • 0002786665 scopus 로고
    • Spline approximation by quasi-interpolants
    • de Boor C., and Fix G. Spline approximation by quasi-interpolants. J. Approx. Theory 8 (1973) 19-45
    • (1973) J. Approx. Theory , vol.8 , pp. 19-45
    • de Boor, C.1    Fix, G.2
  • 30
    • 0000671861 scopus 로고
    • A new convergence proof for the multigrid method including the V-cycle
    • Braess D., and Hackbusch W. A new convergence proof for the multigrid method including the V-cycle. SIAM J. Numer. Anal. 20 (1983) 967-975
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 967-975
    • Braess, D.1    Hackbusch, W.2
  • 31
    • 0014749272 scopus 로고
    • Estimation of linear functionals on Sobolev spaces with applications to Fourier transform and spline interpolation
    • Bramble J.H., and Hilbert S.R. Estimation of linear functionals on Sobolev spaces with applications to Fourier transform and spline interpolation. SIAM J. Numer. Anal. 7 (1970) 112-124
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 112-124
    • Bramble, J.H.1    Hilbert, S.R.2
  • 32
    • 0000497851 scopus 로고
    • Bounds for a class of linear functionals with applications to Hermite interpolation
    • Bramble J.H., and Hilbert S.R. Bounds for a class of linear functionals with applications to Hermite interpolation. Numer. Math. 16 (1971) 362-369
    • (1971) Numer. Math. , vol.16 , pp. 362-369
    • Bramble, J.H.1    Hilbert, S.R.2
  • 33
    • 84966234195 scopus 로고
    • Parallel multilevel preconditioners
    • Bramble J.H., Pasciak J.E., and Xu J. Parallel multilevel preconditioners. Math. Comp. 55 (1990) 1-22
    • (1990) Math. Comp. , vol.55 , pp. 1-22
    • Bramble, J.H.1    Pasciak, J.E.2    Xu, J.3
  • 34
    • 0004219794 scopus 로고
    • Longman Scientific and Technical, New York
    • Bramble J.H. Multigrid Methods (1993), Longman Scientific and Technical, New York
    • (1993) Multigrid Methods
    • Bramble, J.H.1
  • 35
    • 84966233568 scopus 로고
    • Multilevel adaptive solutions to boundary value problems
    • Brandt A. Multilevel adaptive solutions to boundary value problems. Math. Comp. 31 (1977) 333-390
    • (1977) Math. Comp. , vol.31 , pp. 333-390
    • Brandt, A.1
  • 37
    • 70350315109 scopus 로고
    • Padé approximations
    • Ciarlet P.G., and Lions J.L. (Eds), North-Holland, New York
    • Brezinski C., and Van Iseghem J. Padé approximations. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis III (1994), North-Holland, New York
    • (1994) Handbook of Numerical Analysis , vol.III
    • Brezinski, C.1    Van Iseghem, J.2
  • 38
    • 84956135234 scopus 로고
    • Approximation of functions of n-variables by quasi-polynomials
    • Brudnyi Y. Approximation of functions of n-variables by quasi-polynomials. Math. USSR Izv. 4 (1970) 568-586
    • (1970) Math. USSR Izv. , vol.4 , pp. 568-586
    • Brudnyi, Y.1
  • 39
    • 0020737631 scopus 로고
    • The Laplacian pyramid as a compact image code
    • Burt P., and Adelson E. The Laplacian pyramid as a compact image code. IEEE Trans. Comm. 31 (1983) 482-540
    • (1983) IEEE Trans. Comm. , vol.31 , pp. 482-540
    • Burt, P.1    Adelson, E.2
  • 41
    • 0000987709 scopus 로고
    • Jackson and Bernstein type inequalities for families of commutative operators in Banach spaces
    • Butzer P.L., and Scherer K. Jackson and Bernstein type inequalities for families of commutative operators in Banach spaces. J. Approx. Theory 5 (1972) 308-342
    • (1972) J. Approx. Theory , vol.5 , pp. 308-342
    • Butzer, P.L.1    Scherer, K.2
  • 42
    • 1642599453 scopus 로고    scopus 로고
    • Wavelet-based adaptive methods for advection-diffusion problems
    • Canuto C., and Cravero I. Wavelet-based adaptive methods for advection-diffusion problems. Math. Mod. Meth. Appl. Sci. 7 (1997) 265-289
    • (1997) Math. Mod. Meth. Appl. Sci. , vol.7 , pp. 265-289
    • Canuto, C.1    Cravero, I.2
  • 43
    • 0007372257 scopus 로고    scopus 로고
    • The wavelet element method. Part I: construction and analysis
    • Canuto C., Tabacco A., and Urban K. The wavelet element method. Part I: construction and analysis. Appl. Comp. Harm. Anal. 6 (1999) 1-52
    • (1999) Appl. Comp. Harm. Anal. , vol.6 , pp. 1-52
    • Canuto, C.1    Tabacco, A.2    Urban, K.3
  • 44
  • 46
    • 0001051450 scopus 로고
    • An algorithm for high speed curve generation
    • Chaitkin G.M. An algorithm for high speed curve generation. Comp. Graph. and Image Process 3 (1974) 346-349
    • (1974) Comp. Graph. and Image Process , vol.3 , pp. 346-349
    • Chaitkin, G.M.1
  • 49
    • 0002154873 scopus 로고
    • Wavelets on a bounded interval
    • Braess D., and Schumaker L. (Eds), Birkhäuser, Boston
    • Chui C.K., and Quak E. Wavelets on a bounded interval. In: Braess D., and Schumaker L. (Eds). Numerical Methods of Approximation Theory (1992), Birkhäuser, Boston 57-76
    • (1992) Numerical Methods of Approximation Theory , pp. 57-76
    • Chui, C.K.1    Quak, E.2
  • 50
    • 36148972266 scopus 로고
    • A general framework for compactly supported splines and wavelets
    • Chui C.K., and Wang Y. A general framework for compactly supported splines and wavelets. J. Approx. Theory 71 (1992) 263-304
    • (1992) J. Approx. Theory , vol.71 , pp. 263-304
    • Chui, C.K.1    Wang, Y.2
  • 52
    • 0001198078 scopus 로고
    • Basic error estimate for the finite element method
    • Ciarlet P.G., and Lions J.L. (Eds), Elsevier, Amsterdam
    • Ciarlet P.G. Basic error estimate for the finite element method. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis II (1991), Elsevier, Amsterdam
    • (1991) Handbook of Numerical Analysis , vol.II
    • Ciarlet, P.G.1
  • 53
    • 0040701762 scopus 로고
    • Constructive function theory and spline systems
    • Ciesielski Z. Constructive function theory and spline systems. Studia Math. 52 (1973) 277-302
    • (1973) Studia Math. , vol.52 , pp. 277-302
    • Ciesielski, Z.1
  • 55
    • 0016541865 scopus 로고
    • Approximation by finite element functions using local regularizations
    • Clement P. Approximation by finite element functions using local regularizations. RAIRO Mod. Math. Anal. Num. 2 (1975) 77-84
    • (1975) RAIRO Mod. Math. Anal. Num. , vol.2 , pp. 77-84
    • Clement, P.1
  • 57
    • 70350266166 scopus 로고    scopus 로고
    • Tree-structured approximation and optimal encoding
    • Preprint LAN/UPMC, to appear in
    • Preprint LAN/UPMC, to appear in. Cohen A., Dahmen W., Daubechies I., and DeVore R. Tree-structured approximation and optimal encoding. App. Comp. Harm. Anal. (2000)
    • (2000) App. Comp. Harm. Anal.
    • Cohen, A.1    Dahmen, W.2    Daubechies, I.3    DeVore, R.4
  • 59
    • 70350330244 scopus 로고    scopus 로고
    • Multiscale methods on bounded domains
    • Preprint LAN/UPMC, to appear in
    • Preprint LAN/UPMC, to appear in. Cohen A., Dahmen W., and DeVore R. Multiscale methods on bounded domains. Trans. Amer. Math. Soc. (2000)
    • (2000) Trans. Amer. Math. Soc.
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 61
    • 70350331533 scopus 로고    scopus 로고
    • Adaptive wavelet methods for elliptic equations - Convergence rates
    • Preprint LAN/UPMC 98049, to appear in
    • Preprint LAN/UPMC 98049, to appear in. Cohen A., Dahmen W., and DeVore R. Adaptive wavelet methods for elliptic equations - Convergence rates. Math. Comp. (2000)
    • (2000) Math. Comp.
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 62
    • 0027840161 scopus 로고
    • Wavelets and fast wavelet transforms on an interval
    • Cohen A., Daubechies I., and Vial P. Wavelets and fast wavelet transforms on an interval. Appl. Comp. Harm. Anal. 1 (1993) 54-81
    • (1993) Appl. Comp. Harm. Anal. , vol.1 , pp. 54-81
    • Cohen, A.1    Daubechies, I.2    Vial, P.3
  • 63
    • 84974002026 scopus 로고
    • A stability criterion for biorthogonal wavelets and their related subband coding schemes
    • Cohen A., and Daubechies I. A stability criterion for biorthogonal wavelets and their related subband coding schemes. Duke Math. J. 68 (1992) 313-335
    • (1992) Duke Math. J. , vol.68 , pp. 313-335
    • Cohen, A.1    Daubechies, I.2
  • 64
    • 0030502820 scopus 로고    scopus 로고
    • A new technique to estimate the regularity of refinable functions
    • Cohen A., and Daubechies I. A new technique to estimate the regularity of refinable functions. Rev. Mat. Iberoamericana 12 (1996) 527-591
    • (1996) Rev. Mat. Iberoamericana , vol.12 , pp. 527-591
    • Cohen, A.1    Daubechies, I.2
  • 67
    • 0004058578 scopus 로고    scopus 로고
    • Quadratures singulieres et fonctions d'echelle
    • Sér. I
    • Sér. I. Cohen, and Ezzine. Quadratures singulieres et fonctions d'echelle. C. R. Acad. Sci. Paris 323 (1996) 829-834
    • (1996) C. R. Acad. Sci. Paris , vol.323 , pp. 829-834
    • Cohen1    Ezzine2
  • 68
    • 0033239768 scopus 로고    scopus 로고
    • On the regularity of multivariate refinable functions
    • Cohen A., Gröchenig K., and Villemoes L. On the regularity of multivariate refinable functions. Constr. Approx. 15 (1999) 241-255
    • (1999) Constr. Approx. , vol.15 , pp. 241-255
    • Cohen, A.1    Gröchenig, K.2    Villemoes, L.3
  • 69
    • 0033297111 scopus 로고    scopus 로고
    • Wavelet adaptive methods for elliptic problems - preconditioning and adaptivity
    • Cohen A., and Masson R. Wavelet adaptive methods for elliptic problems - preconditioning and adaptivity. SIAM J. Sci. Comput. 21 (1999) 1006-1026
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 1006-1026
    • Cohen, A.1    Masson, R.2
  • 71
    • 70350328368 scopus 로고    scopus 로고
    • Wavelet methods for elliptic problems - boundary conditions and domain decomposition
    • Preprint LAN/UPMC 98007, to appear in
    • Preprint LAN/UPMC 98007, to appear in. Cohen A., and Masson R. Wavelet methods for elliptic problems - boundary conditions and domain decomposition. Numer. Math. (2000)
    • (2000) Numer. Math.
    • Cohen, A.1    Masson, R.2
  • 73
    • 21344492293 scopus 로고
    • Compactly supported wavelets with hexagonal symmetry
    • Cohen A., and Schlenker J.M. Compactly supported wavelets with hexagonal symmetry. Constr. Approx. 9 (1993) 209-236
    • (1993) Constr. Approx. , vol.9 , pp. 209-236
    • Cohen, A.1    Schlenker, J.M.2
  • 75
  • 76
    • 0031623074 scopus 로고    scopus 로고
    • Besov regularity for elliptic boundary value problems with variable coefficients
    • Dahlke S. Besov regularity for elliptic boundary value problems with variable coefficients. Manuscripta Math. 95 (1998) 59-77
    • (1998) Manuscripta Math. , vol.95 , pp. 59-77
    • Dahlke, S.1
  • 77
    • 0001786643 scopus 로고    scopus 로고
    • Besov regularity for elliptic boundary value problems on polygonal domains
    • Dahlke S. Besov regularity for elliptic boundary value problems on polygonal domains. Appl. Math. Lett. 12 (1999) 31-36
    • (1999) Appl. Math. Lett. , vol.12 , pp. 31-36
    • Dahlke, S.1
  • 78
    • 0031069391 scopus 로고    scopus 로고
    • Stable multiscale bases and local error estimation for elliptic problems
    • Dahlke S., Dahmen W., Hochmuth R., and Schneider R. Stable multiscale bases and local error estimation for elliptic problems. Appl. Numer. Math. 23 (1997) 21-48
    • (1997) Appl. Numer. Math. , vol.23 , pp. 21-48
    • Dahlke, S.1    Dahmen, W.2    Hochmuth, R.3    Schneider, R.4
  • 79
    • 0002494590 scopus 로고    scopus 로고
    • Besov regularity for elliptic boundary value problems
    • Dahlke S., and DeVore R. Besov regularity for elliptic boundary value problems. Comm. in PDE's 22 (1996) 1-16
    • (1996) Comm. in PDE's , vol.22 , pp. 1-16
    • Dahlke, S.1    DeVore, R.2
  • 80
    • 1842484444 scopus 로고    scopus 로고
    • Stability of multiscale transforms
    • Dahmen W. Stability of multiscale transforms. J. Fourier Anal. Appl. 2 (1996) 341-361
    • (1996) J. Fourier Anal. Appl. , vol.2 , pp. 341-361
    • Dahmen, W.1
  • 81
    • 85011480386 scopus 로고    scopus 로고
    • Wavelets and multiscale methods for operator equations
    • Dahmen W. Wavelets and multiscale methods for operator equations. Acta Numerica (1997) 55-228
    • (1997) Acta Numerica , pp. 55-228
    • Dahmen, W.1
  • 82
    • 0034354827 scopus 로고    scopus 로고
    • Biorthogonal multiwavelets on the interval: Cubic Hermite splines
    • Dahmen W., Han B., Jia R.-Q., and Kunoth A. Biorthogonal multiwavelets on the interval: Cubic Hermite splines. Constr. Approx. 16 (2000) 221-259
    • (2000) Constr. Approx. , vol.16 , pp. 221-259
    • Dahmen, W.1    Han, B.2    Jia, R.-Q.3    Kunoth, A.4
  • 83
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • Dahmen W., and Kunoth A. Multilevel preconditioning. Numer. Math. 63 (1992) 315-344
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 84
    • 0000656283 scopus 로고    scopus 로고
    • Operator equations, multiscale concepts and complexity
    • 1995 AMS-SIAM Summer Seminar, Math. of Numer. Anal.
    • Dahmen W., Kunoth A., and Schneider R. Operator equations, multiscale concepts and complexity. 1995 AMS-SIAM Summer Seminar, Math. of Numer. Anal. Amer. Math. Soc., Lectures in Appl. Math. 32 (1996) 225-261
    • (1996) Amer. Math. Soc., Lectures in Appl. Math. , vol.32 , pp. 225-261
    • Dahmen, W.1    Kunoth, A.2    Schneider, R.3
  • 85
    • 0030385589 scopus 로고    scopus 로고
    • A wavelet Galerkin method for the Stokes problem
    • Dahmen W., Kunoth A., and Urban K. A wavelet Galerkin method for the Stokes problem. Computing 56 (1996) 259-302
    • (1996) Computing , vol.56 , pp. 259-302
    • Dahmen, W.1    Kunoth, A.2    Urban, K.3
  • 86
    • 0001787026 scopus 로고    scopus 로고
    • Biorthogonal spline-wavelets on the interval
    • Stability and moment conditions
    • Dahmen W., Kunoth A., and Urban K. Biorthogonal spline-wavelets on the interval. Stability and moment conditions. Appl. Comp. Harm. Anal. 6 (1999) 132-196
    • (1999) Appl. Comp. Harm. Anal. , vol.6 , pp. 132-196
    • Dahmen, W.1    Kunoth, A.2    Urban, K.3
  • 87
    • 0004972688 scopus 로고
    • Subdivision algorithms for the generation of box spline surfaces
    • Dahmen W., and Micchelli C.A. Subdivision algorithms for the generation of box spline surfaces. Computer Aided Geom. Design 1 (1984) 115-129
    • (1984) Computer Aided Geom. Design , vol.1 , pp. 115-129
    • Dahmen, W.1    Micchelli, C.A.2
  • 88
    • 0027574359 scopus 로고
    • Using the refinement equation for evaluating integrals of wavelets
    • Dahmen W., and Micchelli C.A. Using the refinement equation for evaluating integrals of wavelets. SIAM J. Numer. Anal. 30 (1993) 507-537
    • (1993) SIAM J. Numer. Anal. , vol.30 , pp. 507-537
    • Dahmen, W.1    Micchelli, C.A.2
  • 89
    • 0000827236 scopus 로고
    • Wavelet methods for pseudodifferential equations II: Matrix compression and fast solution
    • Dahmen W., Prössdorf S., and Schneider R. Wavelet methods for pseudodifferential equations II: Matrix compression and fast solution. Adv. Comput. Math. 1 (1993) 259-335
    • (1993) Adv. Comput. Math. , vol.1 , pp. 259-335
    • Dahmen, W.1    Prössdorf, S.2    Schneider, R.3
  • 90
    • 51249161722 scopus 로고
    • Wavelet approximation methods for pseudodifferential equations I: Stability and convergence
    • Dahmen W., Prössdorf S., and Schneider R. 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    Prössdorf, S.2    Schneider, R.3
  • 91
    • 0000619262 scopus 로고    scopus 로고
    • Wavelets with complementary boundary conditions - function spaces on the cube
    • Dahmen W., and Schneider R. Wavelets with complementary boundary conditions - function spaces on the cube. Results in Math. 34 (1998) 255-293
    • (1998) Results in Math. , vol.34 , pp. 255-293
    • Dahmen, W.1    Schneider, R.2
  • 92
    • 0033426280 scopus 로고    scopus 로고
    • Composite wavelet bases for operator equations
    • Dahmen W., and Schneider R. Composite wavelet bases for operator equations. Math. Comp. 68 (1999) 1533-1567
    • (1999) Math. Comp. , vol.68 , pp. 1533-1567
    • Dahmen, W.1    Schneider, R.2
  • 93
    • 0033233501 scopus 로고    scopus 로고
    • Wavelets on manifold I. Construction and domain decomposition
    • Dahmen W., and Schneider R. Wavelets on manifold I. Construction and domain decomposition. SIAM J. Math. Anal. 31 (1999) 184-230
    • (1999) SIAM J. Math. Anal. , vol.31 , pp. 184-230
    • Dahmen, W.1    Schneider, R.2
  • 94
    • 0000930347 scopus 로고    scopus 로고
    • Element by element construction of wavelets satisfying stability and moment conditions
    • Dahmen W., and Stevenson R. Element by element construction of wavelets satisfying stability and moment conditions. SIAM J. Numer. Anal. 37 (1999) 319-352
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 319-352
    • Dahmen, W.1    Stevenson, R.2
  • 95
    • 84990575058 scopus 로고
    • Orthonormal bases of compactly supported wavelets
    • Daubechies I. Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988) 909-996
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 909-996
    • Daubechies, I.1
  • 97
    • 0000364986 scopus 로고
    • Two scale difference equations I. Existence and global regularity of solutions
    • Daubechies I., and Lagarias J. Two scale difference equations I. Existence and global regularity of solutions. SIAM J. Math. Anal. 22 (1991) 1388-1410
    • (1991) SIAM J. Math. Anal. , vol.22 , pp. 1388-1410
    • Daubechies, I.1    Lagarias, J.2
  • 98
    • 0000160525 scopus 로고
    • Two scale difference equations II. Local regularity, infinite products of matrices and fractals
    • Daubechies I., and Lagarias J. Two scale difference equations II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23 (1992) 1031-1079
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1031-1079
    • Daubechies, I.1    Lagarias, J.2
  • 99
    • 18344410543 scopus 로고    scopus 로고
    • Factoring wavelet transform into lifting steps
    • Daubechies I., and Sweldens W. Factoring wavelet transform into lifting steps. J. Fourier Anal. Appl. 4 (1998) 247-269
    • (1998) J. Fourier Anal. Appl. , vol.4 , pp. 247-269
    • Daubechies, I.1    Sweldens, W.2
  • 101
    • 0001720260 scopus 로고
    • A boundedness criterion for generalized Calderon-Zygmund operators
    • David G., and Journé J.L. A boundedness criterion for generalized Calderon-Zygmund operators. Ann. of Math. 120 (1984) 371-397
    • (1984) Ann. of Math. , vol.120 , pp. 371-397
    • David, G.1    Journé, J.L.2
  • 102
    • 0001446381 scopus 로고
    • Les espaces de type de Beppo Levi
    • Deny J., and Lions J.L. Les espaces de type de Beppo Levi. Ann. Inst. Fourier 5 (1954) 305-370
    • (1954) Ann. Inst. Fourier , vol.5 , pp. 305-370
    • Deny, J.1    Lions, J.L.2
  • 104
    • 85009724776 scopus 로고    scopus 로고
    • Non-linear approximation
    • DeVore R. Non-linear approximation. Acta Numerica 7 (1998) 51-150
    • (1998) Acta Numerica , vol.7 , pp. 51-150
    • DeVore, R.1
  • 105
    • 0001220724 scopus 로고
    • Compression of wavelet decompositions
    • DeVore R., Jawerth B., and Popov V. Compression of wavelet decompositions. Amer. J. Math. 114 (1992) 737-785
    • (1992) Amer. J. Math. , vol.114 , pp. 737-785
    • DeVore, R.1    Jawerth, B.2    Popov, V.3
  • 107
    • 0002225802 scopus 로고
    • High order regularity for conservation laws
    • DeVore R., and Lucier B. High order regularity for conservation laws. Indiana Math. J. 39 (1990) 413-430
    • (1990) Indiana Math. J. , vol.39 , pp. 413-430
    • DeVore, R.1    Lucier, B.2
  • 109
    • 0003337602 scopus 로고
    • Free multivariate splines
    • DeVore R., and Popov V. Free multivariate splines. Constr. Approx. 3 (1988) 239-248
    • (1988) Constr. Approx. , vol.3 , pp. 239-248
    • DeVore, R.1    Popov, V.2
  • 110
  • 111
    • 0001604851 scopus 로고
    • Interpolation spaces and nonlinear approximation
    • Function Spaces and Applications. Cwikel M., Peetre J., Sagher Y., and Wallin H. (Eds), Springer-Verlag, New York
    • DeVore R., and Popov V. Interpolation spaces and nonlinear approximation. In: Cwikel M., Peetre J., Sagher Y., and Wallin H. (Eds). Function Spaces and Applications. Lecture Notes in Math. 1302 (1988), Springer-Verlag, New York 191-205
    • (1988) Lecture Notes in Math. , vol.1302 , pp. 191-205
    • DeVore, R.1    Popov, V.2
  • 114
    • 84966250951 scopus 로고
    • Degree of adaptive approximation
    • DeVore R., and Yu X.M. Degree of adaptive approximation. Math. Comp. 55 (1990) 625-635
    • (1990) Math. Comp. , vol.55 , pp. 625-635
    • DeVore, R.1    Yu, X.M.2
  • 116
    • 0033438951 scopus 로고    scopus 로고
    • Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets
    • Donovan G., Geronimo J., and Hardin D. Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. SIAM J. Math. Anal. 30 (1999) 1029-1056
    • (1999) SIAM J. Math. Anal. , vol.30 , pp. 1029-1056
    • Donovan, G.1    Geronimo, J.2    Hardin, D.3
  • 117
    • 1542639888 scopus 로고    scopus 로고
    • A convergent adaptive algorithm for Poisson's equation
    • Doerfler W. A convergent adaptive algorithm for Poisson's equation. SIAM J. Numer. Anal. 33 (1996) 1106-1124
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1106-1124
    • Doerfler, W.1
  • 120
    • 14244261558 scopus 로고    scopus 로고
    • A construction of biorthogonal functions to B-splines with multiple knots
    • Dyn N. A construction of biorthogonal functions to B-splines with multiple knots. Appl. Comp. Harm. Anal. 8 (2000) 24-31
    • (2000) Appl. Comp. Harm. Anal. , vol.8 , pp. 24-31
    • Dyn, N.1
  • 121
    • 0000541265 scopus 로고
    • Analysis of uniform binary subdivision schemes for curve design
    • Dyn N., Gregory J., and Levin D. Analysis of uniform binary subdivision schemes for curve design. Constr. Approx. 7 (1991) 127-147
    • (1991) Constr. Approx. , vol.7 , pp. 127-147
    • Dyn, N.1    Gregory, J.2    Levin, D.3
  • 122
    • 0001301724 scopus 로고
    • Sobolev characterization of solutions of dilation equations
    • Eirola T. Sobolev characterization of solutions of dilation equations. SIAM J. Math. Anal. 23 (1992) 1015-1030
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1015-1030
    • Eirola, T.1
  • 123
    • 0009522795 scopus 로고
    • Introduction to adaptive methods for differential equations
    • Cambridge University Press, Oxford
    • Eriksson K., Estep D., Hansbo P., and Johnson C. Introduction to adaptive methods for differential equations. Acta Numerica (1995), Cambridge University Press, Oxford 105-158
    • (1995) Acta Numerica , pp. 105-158
    • Eriksson, K.1    Estep, D.2    Hansbo, P.3    Johnson, C.4
  • 124
    • 0001038302 scopus 로고
    • The speed of convergence of one iterative process
    • Fedorenko R.P. The speed of convergence of one iterative process. USSR Comp. Math. Math. Phys. 4 (1964) 1092-1096
    • (1964) USSR Comp. Math. Math. Phys. , vol.4 , pp. 1092-1096
    • Fedorenko, R.P.1
  • 125
    • 0003292476 scopus 로고
    • Littlewood-Paley Theory and the Study of Function Spaces
    • Amer. Math. Soc.
    • Frazier M., Jawerth B., and Weiss G. Littlewood-Paley Theory and the Study of Function Spaces. CBMS Conference Lecture Notes 79 (1991), Amer. Math. Soc.
    • (1991) CBMS Conference Lecture Notes , vol.79
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 127
    • 0000007919 scopus 로고    scopus 로고
    • A comparison of multiresolution and classical one-dimensional homogeneization schemes
    • Gilbert A. A comparison of multiresolution and classical one-dimensional homogeneization schemes. Appl. Comp. Harm. Anal. 5 (1998) 1-35
    • (1998) Appl. Comp. Harm. Anal. , vol.5 , pp. 1-35
    • Gilbert, A.1
  • 128
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • Greengard L., and Rokhlin V. A fast algorithm for particle simulations. J. Comp. Phys. 325 (1987)
    • (1987) J. Comp. Phys. , vol.325
    • Greengard, L.1    Rokhlin, V.2
  • 131
    • 0001617415 scopus 로고
    • On the fast matrix multiplication in the boundary element method by panel clustering
    • Hackbusch W., and Nowak Z.P. On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54 (1989) 463-491
    • (1989) Numer. Math. , vol.54 , pp. 463-491
    • Hackbusch, W.1    Nowak, Z.P.2
  • 132
    • 44949266025 scopus 로고
    • Discrete multiresolution and generalized wavelets
    • Harten A. Discrete multiresolution and generalized wavelets. J. Appl. Numer. Math. 12 (1993) 153-193
    • (1993) J. Appl. Numer. Math. , vol.12 , pp. 153-193
    • Harten, A.1
  • 133
    • 84990727055 scopus 로고
    • Multiresolution algorithms for the numerical solution of hyperbolic conservation laws
    • Harten A. Multiresolution algorithms for the numerical solution of hyperbolic conservation laws. Comm. Pure Appl. Math. 48 (1995) 1305-1342
    • (1995) Comm. Pure Appl. Math. , vol.48 , pp. 1305-1342
    • Harten, A.1
  • 134
    • 0000917785 scopus 로고    scopus 로고
    • Multiresolution representation of data II: Generalized framework
    • Harten A. Multiresolution representation of data II: Generalized framework. SIAM J. Numer. Anal. 33 (1996) 1205-1256
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1205-1256
    • Harten, A.1
  • 135
    • 0000289305 scopus 로고
    • Pointwise smoothness, two-microlocalization and wavelet coefficients
    • Jaffard S. Pointwise smoothness, two-microlocalization and wavelet coefficients. Publ. Mat. 35 (1991) 155-168
    • (1991) Publ. Mat. , vol.35 , pp. 155-168
    • Jaffard, S.1
  • 136
    • 0026909957 scopus 로고
    • Wavelet methods for fast resolution of elliptic problems
    • Jaffard S. Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal. 29 (1992) 965-986
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 965-986
    • Jaffard, S.1
  • 137
    • 22844456721 scopus 로고    scopus 로고
    • Smoothness of multivariate refinable functions in Sobolev spaces
    • JIA R.Q. Smoothness of multivariate refinable functions in Sobolev spaces. Trans. Amer. Math. Soc. 351 (1999) 4089-4112
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 4089-4112
    • JIA, R.Q.1
  • 138
    • 0032344506 scopus 로고    scopus 로고
    • Multivariate refinement equations and convergence of subdivision schemes
    • Jia R.Q., and Han B. Multivariate refinement equations and convergence of subdivision schemes. SIAM J. Math. Anal. 29 (1998) 1177-1199
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1177-1199
    • Jia, R.Q.1    Han, B.2
  • 139
    • 0003106786 scopus 로고
    • Approximation by multi-integer translates of functions having global support
    • Jia R.Q., and Lei J.J. Approximation by multi-integer translates of functions having global support. J. Approx. Theory 72 (1993) 2-23
    • (1993) J. Approx. Theory , vol.72 , pp. 2-23
    • Jia, R.Q.1    Lei, J.J.2
  • 140
  • 141
    • 0007071399 scopus 로고
    • On the equivalence of the K-functional and moduli of continuity and some applications
    • Constructive Theory of Functions of Several Variables, Springer-Verlag, New York
    • Johnen H., and Scherer K. On the equivalence of the K-functional and moduli of continuity and some applications. Constructive Theory of Functions of Several Variables. Lecture Notes in Math. 571 (1976), Springer-Verlag, New York
    • (1976) Lecture Notes in Math. , vol.571
    • Johnen, H.1    Scherer, K.2
  • 142
    • 70350266165 scopus 로고
    • Teoria Constructiva de Functiones
    • University of Buenos Aires, Berlin
    • Kahane J.P. Teoria Constructiva de Functiones. Course Notes (1961), University of Buenos Aires, Berlin
    • (1961) Course Notes
    • Kahane, J.P.1
  • 144
    • 0001594654 scopus 로고
    • Multiscale preconditioning - Appending boundary conditions by Lagrange multipliers
    • Kunoth A. Multiscale preconditioning - Appending boundary conditions by Lagrange multipliers. Adv. Comput. Math. 4 (1995) 145-170
    • (1995) Adv. Comput. Math. , vol.4 , pp. 145-170
    • Kunoth, A.1
  • 147
    • 0000720732 scopus 로고
    • Algorithme à base d'ondelettes pour la résolution numérique d'équations aux dérivées partielles à coefficients variables
    • Sér. I
    • Sér. I. Lazaar S., Liandrat J., and Tchamitchian P. Algorithme à base d'ondelettes pour la résolution numérique d'équations aux dérivées partielles à coefficients variables. C. R. Acad. Sci. Paris 319 (1994) 1101-1107
    • (1994) C. R. Acad. Sci. Paris , vol.319 , pp. 1101-1107
    • Lazaar, S.1    Liandrat, J.2    Tchamitchian, P.3
  • 148
    • 0001636694 scopus 로고
    • Ondelettes à localisation exponentielle
    • Lemarié P.G. Ondelettes à localisation exponentielle. J. Math. Pures Appl. 67 (1988) 227-236
    • (1988) J. Math. Pures Appl. , vol.67 , pp. 227-236
    • Lemarié, P.G.1
  • 149
    • 0000423051 scopus 로고
    • Analyses multirésolutions nonorthogonales, commutation entre projecteurs et dérivation et ondelettes vecteurs à divergence nulle
    • Lemarié P.G. Analyses multirésolutions nonorthogonales, commutation entre projecteurs et dérivation et ondelettes vecteurs à divergence nulle. Rev. Mat. Iberoamericana 8 (1992) 221-236
    • (1992) Rev. Mat. Iberoamericana , vol.8 , pp. 221-236
    • Lemarié, P.G.1
  • 150
    • 0000019891 scopus 로고    scopus 로고
    • On the existence of compactly supported dual wavelets
    • Lemarié P.G. On the existence of compactly supported dual wavelets. Appl. Comp. Harm. Anal. 3 (1997) 117-118
    • (1997) Appl. Comp. Harm. Anal. , vol.3 , pp. 117-118
    • Lemarié, P.G.1
  • 151
    • 0000998527 scopus 로고
    • Support des fonctions de base dans une analyse multiresolution
    • Sér. I
    • Sér. I. Lemarié P.G., and Malgouyres G. Support des fonctions de base dans une analyse multiresolution. C. R. Acad. Sci. Paris 213 (1991) 377-380
    • (1991) C. R. Acad. Sci. Paris , vol.213 , pp. 377-380
    • Lemarié, P.G.1    Malgouyres, G.2
  • 155
    • 0042658935 scopus 로고
    • Knot removal for spline curves and surfaces
    • Cheney E.W., Chui C.K., and Schumaker L. (Eds), Academic Press, New York
    • Lyche T. Knot removal for spline curves and surfaces. In: Cheney E.W., Chui C.K., and Schumaker L. (Eds). Approximation Theory VII (1993), Academic Press, New York 207-227
    • (1993) Approximation Theory , vol.VII , pp. 207-227
    • Lyche, T.1
  • 156
    • 0000094031 scopus 로고
    • Adaptativité dynamique sur bases d'ondelettes pour l'approximation d'équations aux dérivées partielles
    • Sér. I
    • Sér. I. Maday Y., Perrier V., and Ravel J.C. Adaptativité dynamique sur bases d'ondelettes pour l'approximation d'équations aux dérivées partielles. C. R. Acad. Sci. Paris 1 (1991) 405-410
    • (1991) C. R. Acad. Sci. Paris , vol.1 , pp. 405-410
    • Maday, Y.1    Perrier, V.2    Ravel, J.C.3
  • 159
    • 0007411796 scopus 로고    scopus 로고
    • Biorthogonal spline wavelets on the interval for the resolution of boundary problems
    • Masson R. Biorthogonal spline wavelets on the interval for the resolution of boundary problems. M3As 6 (1996) 749-791
    • (1996) M3As , vol.6 , pp. 749-791
    • Masson, R.1
  • 160
    • 0004180195 scopus 로고
    • English translation by D.H. Salinger (Cambridge University Press, Cambridge, 1992), Hermann, New York
    • English translation by D.H. Salinger (Cambridge University Press, Cambridge, 1992). Meyer Y. Ondelettes et Opérateurs (1990), Hermann, New York
    • (1990) Ondelettes et Opérateurs
    • Meyer, Y.1
  • 161
    • 0000075686 scopus 로고
    • Ondelettes sur l'intervalle
    • Meyer Y. Ondelettes sur l'intervalle. Rev. Mat. Iberoamericana 7 (1991) 115-134
    • (1991) Rev. Mat. Iberoamericana , vol.7 , pp. 115-134
    • Meyer, Y.1
  • 162
    • 0003448347 scopus 로고
    • English translation by R. Ryan (SIAM, Philadelphia, 1994), Armand Colin, Paris
    • English translation by R. Ryan (SIAM, Philadelphia, 1994). Meyer Y. Ondelettes, Algorithmes et Applications (1992), Armand Colin, Paris
    • (1992) Ondelettes, Algorithmes et Applications
    • Meyer, Y.1
  • 163
    • 67649609957 scopus 로고    scopus 로고
    • Wavelets and fast numerical algorithms
    • Ciarlet P.G., and Lions J.L. (Eds), Elsevier, Paris
    • Meyer Y. Wavelets and fast numerical algorithms. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis V (1997), Elsevier, Paris
    • (1997) Handbook of Numerical Analysis , vol.V
    • Meyer, Y.1
  • 164
    • 0002634427 scopus 로고
    • Rational approximation to |x|
    • Newman D.J. Rational approximation to |x|. Michigan Math. J. 11 (1964) 11-14
    • (1964) Michigan Math. J. , vol.11 , pp. 11-14
    • Newman, D.J.1
  • 166
    • 38249018093 scopus 로고
    • On the degree of nonlinear spline approximation in Besov-Sobolev spaces
    • Oswald P. On the degree of nonlinear spline approximation in Besov-Sobolev spaces. J. Approx. Theory 61 (1990) 131-157
    • (1990) J. Approx. Theory , vol.61 , pp. 131-157
    • Oswald, P.1
  • 171
    • 0000400863 scopus 로고
    • Interpolation of normed Abelian groups
    • Peetre J., and Sparr G. Interpolation of normed Abelian groups. Ann. Mat. Pura Appl. 92 (1972) 217-252
    • (1972) Ann. Mat. Pura Appl. , vol.92 , pp. 217-252
    • Peetre, J.1    Sparr, G.2
  • 172
    • 0001616886 scopus 로고
    • p for p < 1, investigation of the order of rational approximation
    • p for p < 1, investigation of the order of rational approximation. Math. USSR Sb. 50 (1985) 465-494
    • (1985) Math. USSR Sb. , vol.50 , pp. 465-494
    • Peller, V.1
  • 173
    • 0032364927 scopus 로고    scopus 로고
    • Orthogonal wavelet bases adapted for partial differential equations with boundary conditions
    • Perrier V., and Monasse P. Orthogonal wavelet bases adapted for partial differential equations with boundary conditions. SIAM J. Math. Anal. 29 (1998) 1040-1065
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 1040-1065
    • Perrier, V.1    Monasse, P.2
  • 174
    • 77957232248 scopus 로고    scopus 로고
    • Fully discrete multiscale Galerkin BEM
    • Dahmen W., Kurdila A.J., and Oswald P. (Eds), Academic Press, Duham
    • von Petersdorff T., and Schwab C. Fully discrete multiscale Galerkin BEM. In: Dahmen W., Kurdila A.J., and Oswald P. (Eds). Multiscale Wavelet Methods for PDE's (1997), Academic Press, Duham
    • (1997) Multiscale Wavelet Methods for PDE's
    • von Petersdorff, T.1    Schwab, C.2
  • 175
    • 0001843451 scopus 로고
    • Direct and converse theorems for spline and rational approximation and Besov spaces
    • Function Spaces and Applications. Cwikel M., Peetre J., Sagher Y., and Wallin H. (Eds), Springer-Verlag, New York
    • Petrushev P. Direct and converse theorems for spline and rational approximation and Besov spaces. In: Cwikel M., Peetre J., Sagher Y., and Wallin H. (Eds). Function Spaces and Applications. Lecture Notes in Math. 1302 (1988), Springer-Verlag, New York 363-377
    • (1988) Lecture Notes in Math. , vol.1302 , pp. 363-377
    • Petrushev, P.1
  • 177
    • 0002265851 scopus 로고    scopus 로고
    • Bases consisting of rational functions of uniformly bounded degrees or more general functions
    • Preprint Univ. of South. Carolina, to appear in
    • Preprint Univ. of South. Carolina, to appear in. Petrushev P. Bases consisting of rational functions of uniformly bounded degrees or more general functions. J. Funct. Anal. (2000)
    • (2000) J. Funct. Anal.
    • Petrushev, P.1
  • 178
    • 0009987206 scopus 로고
    • Factorization of refinement masks for function vectors
    • Chui C.K., and Schumaker L.L. (Eds), World Scientific, Berlin
    • Plonka G. Factorization of refinement masks for function vectors. In: Chui C.K., and Schumaker L.L. (Eds). Wavelets and Multilevel Approximation (1995), World Scientific, Berlin
    • (1995) Wavelets and Multilevel Approximation
    • Plonka, G.1
  • 179
    • 21144481833 scopus 로고
    • Simple criteria for subdivision scheme
    • Rioul O. Simple criteria for subdivision scheme. SIAM J. Math. Anal. 23 (1992) 1544-1576
    • (1992) SIAM J. Math. Anal. , vol.23 , pp. 1544-1576
    • Rioul, O.1
  • 180
    • 0030242050 scopus 로고    scopus 로고
    • An image multiresolution representation for lossless and lossy compression
    • Said A., and Pearlman W.A. An image multiresolution representation for lossless and lossy compression. IEEE Trans. Image Process 5 (1996) 1303-1310
    • (1996) IEEE Trans. Image Process , vol.5 , pp. 1303-1310
    • Said, A.1    Pearlman, W.A.2
  • 181
    • 0002308457 scopus 로고
    • Contributions to the problem of approximation of equidistant data by analytic functions
    • (part A)
    • (part A). Schoenberg I.J. Contributions to the problem of approximation of equidistant data by analytic functions. Quart. Appl. Math. 4 (1946) 45-99
    • (1946) Quart. Appl. Math. , vol.4 , pp. 45-99
    • Schoenberg, I.J.1
  • 182
    • 0002308457 scopus 로고
    • Contributions to the problem of approximation of equidistant data by analytic functions
    • (part B)
    • (part B). Schoenberg I.J. Contributions to the problem of approximation of equidistant data by analytic functions. Quart. Appl. Math. 4 (1946) 112-141
    • (1946) Quart. Appl. Math. , vol.4 , pp. 112-141
    • Schoenberg, I.J.1
  • 184
    • 0027798110 scopus 로고
    • Embedded image coding using zerotrees of wavelet coefficients
    • Shapiro J. Embedded image coding using zerotrees of wavelet coefficients. IEEE Signal Process 41 (1993) 3445-3462
    • (1993) IEEE Signal Process , vol.41 , pp. 3445-3462
    • Shapiro, J.1
  • 185
    • 0032338133 scopus 로고    scopus 로고
    • Refinable function vectors
    • Shen Z. Refinable function vectors. SIAM J. Math. Anal. 29 (1998) 235-250
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 235-250
    • Shen, Z.1
  • 187
    • 0005115956 scopus 로고    scopus 로고
    • Piecewise linear (pre)-wavelets on nonuniform meshes
    • Lecture Notes in Comput. Sci. Eng. 3. Hackbusch W., and Wittum G. (Eds), Springer-Verlag, Princeton
    • Lecture Notes in Comput. Sci. Eng. 3. Stevenson R. Piecewise linear (pre)-wavelets on nonuniform meshes. In: Hackbusch W., and Wittum G. (Eds). Multigrid Methods V (1998), Springer-Verlag, Princeton 306-319
    • (1998) Multigrid Methods , vol.V , pp. 306-319
    • Stevenson, R.1
  • 188
    • 0031073828 scopus 로고    scopus 로고
    • Experiments in 3D with a three point hierarchical basis preconditioner
    • Stevenson R. Experiments in 3D with a three point hierarchical basis preconditioner. Appl. Numer. Math. 23 (1997) 159-175
    • (1997) Appl. Numer. Math. , vol.23 , pp. 159-175
    • Stevenson, R.1
  • 189
    • 0014563596 scopus 로고
    • Fourier analysis of the finite element method in Ritz-Galerkin theory
    • Strang G., and Fix G. Fourier analysis of the finite element method in Ritz-Galerkin theory. Stud. Appl. Math. 48 (1969) 265-273
    • (1969) Stud. Appl. Math. , vol.48 , pp. 265-273
    • Strang, G.1    Fix, G.2
  • 191
    • 0028485506 scopus 로고
    • Quadrature formulae and asymptotic error expansions for wavelet approximation of smooth functions
    • Sweldens W., and Piessens R. Quadrature formulae and asymptotic error expansions for wavelet approximation of smooth functions. SIAM J. Numer. Anal. 31 (1994) 2140-2164
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 2140-2164
    • Sweldens, W.1    Piessens, R.2
  • 192
    • 30244489068 scopus 로고    scopus 로고
    • The lifting scheme: A custom design construction of biorthogonal wavelets
    • Sweldens W. The lifting scheme: A custom design construction of biorthogonal wavelets. Appl. Comp. Harm. Anal. 3 (1996) 186-200
    • (1996) Appl. Comp. Harm. Anal. , vol.3 , pp. 186-200
    • Sweldens, W.1
  • 193
    • 0032388955 scopus 로고    scopus 로고
    • The lifting scheme: A construction of second generation wavelets
    • Sweldens W. The lifting scheme: A construction of second generation wavelets. SIAM J. Math. Anal. 29 (1998) 511-546
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 511-546
    • Sweldens, W.1
  • 194
    • 0030495231 scopus 로고    scopus 로고
    • Inversion explicite de certains operateurs elliptiques
    • Tchamitchian P. Inversion explicite de certains operateurs elliptiques. SIAM J. Math. Anal. 27 (1996) 1680-1703
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1680-1703
    • Tchamitchian, P.1
  • 195
    • 0005620566 scopus 로고    scopus 로고
    • Wavelets functions and operators
    • Erlebacher G., Hussaini Y., and Jameson L. (Eds), Oxford University Press, Cambridge
    • Tchamitchian P. Wavelets functions and operators. In: Erlebacher G., Hussaini Y., and Jameson L. (Eds). Wavelets, Theory and Applications (1996), Oxford University Press, Cambridge 87-178
    • (1996) Wavelets, Theory and Applications , pp. 87-178
    • Tchamitchian, P.1
  • 197
    • 34249754212 scopus 로고
    • On divergence-free wavelets
    • Urban K. On divergence-free wavelets. Advances in Comp. Math. 4 (1995) 51-82
    • (1995) Advances in Comp. Math. , vol.4 , pp. 51-82
    • Urban, K.1
  • 199
    • 0028423814 scopus 로고
    • A posteriori error estimation and adaptive mesh refinement techniques
    • Verfurth R. A posteriori error estimation and adaptive mesh refinement techniques. J. Comput. Appl. Math. 50 (1994) 67-83
    • (1994) J. Comput. Appl. Math. , vol.50 , pp. 67-83
    • Verfurth, R.1
  • 200
    • 0042275098 scopus 로고
    • Wavelet analysis of two-scale refinement equations
    • Villemoes L. Wavelet analysis of two-scale refinement equations. SIAM J. Math. Anal. 25 (1994) 1433-1460
    • (1994) SIAM J. Math. Anal. , vol.25 , pp. 1433-1460
    • Villemoes, L.1
  • 201
    • 0026765549 scopus 로고
    • On the regularity of wavelets
    • Volkmer H. On the regularity of wavelets. IEEE Trans. Inform. Theory 38 (1992) 872-876
    • (1992) IEEE Trans. Inform. Theory , vol.38 , pp. 872-876
    • Volkmer, H.1
  • 203
    • 34250126304 scopus 로고
    • On the multi-level splitting of finite element spaces
    • Yserantant H. On the multi-level splitting of finite element spaces. Numer. Math. 49 (1986) 379-412
    • (1986) Numer. Math. , vol.49 , pp. 379-412
    • Yserantant, H.1
  • 204
    • 84971922635 scopus 로고
    • Old and new convergence proof for multigrid methods
    • Cambridge University Press, New York
    • Yserantant H. Old and new convergence proof for multigrid methods. Acta Numerica (1993), Cambridge University Press, New York 285-326
    • (1993) Acta Numerica , pp. 285-326
    • Yserantant, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.