메뉴 건너뛰기




Volumn 31, Issue 1, 1999, Pages 184-230

Wavelets on manifolds I: Construction and domain decomposition

Author keywords

Biorthogonal wavelet bases; Boundary integral equations; Complementary boundary conditions; Domain decomposition; Norm equivalences; Sobolev spaces on manifolds; Topological isomorphisms

Indexed keywords


EID: 0033233501     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098333451     Document Type: Article
Times cited : (145)

References (46)
  • 1
    • 0003337186 scopus 로고
    • Sobolev Spaces
    • Academic Press, London, New York
    • R. A. ADAMS, Sobolev Spaces. Pure and Applied Mathematics, Vol. 65, Academic Press, London, New York, 1978.
    • (1978) Pure and Applied Mathematics , vol.65
    • Adams, R.A.1
  • 2
    • 0000139676 scopus 로고
    • Wavelet-like bases for the fast solution of second-kind integral equations
    • B. ALPERT, G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Wavelet-like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Statist. Comput., 14 (1993), pp. 159-184.
    • (1993) SIAM J. Sci. Statist. Comput. , vol.14 , pp. 159-184
    • Alpert, B.1    Beylkin, G.2    Coifman, R.3    Rokhlin, V.4
  • 5
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms I
    • G. BEYLKIN, R. R. COIFMAN, AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
    • (1991) Comm. Pure Appl. Math. , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.R.2    Rokhlin, V.3
  • 6
    • 0001701058 scopus 로고    scopus 로고
    • A posteriori error estimates for elliptic problems in two and three space dimensions
    • F. BORNEMANN, B. ERDMANN, AND R. KORNHUBER, A posteriori error estimates for elliptic problems in two and three space dimensions, SIAM J. Numer. Anal., 33 (1996), pp. 1188-1204.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1188-1204
    • Bornemann, F.1    Erdmann, B.2    Kornhuber, R.3
  • 7
    • 0007372257 scopus 로고    scopus 로고
    • The wavelet element method part I: Construction and analysis
    • C. CANUTO, A. TABACCO, AND K. URBAN, The wavelet element method part I: Construction and analysis, Appl. Comput. Harmon. Anal., 6 (1999), pp. 1-52.
    • (1999) Appl. Comput. Harmon. Anal. , vol.6 , pp. 1-52
    • Canuto, C.1    Tabacco, A.2    Urban, K.3
  • 9
    • 0002162649 scopus 로고
    • Spline bases in classical function spaces on compact C∞ manifolds, Parts I and II
    • Z. CIESIELSKI AND T. FIGIEL, Spline bases in classical function spaces on compact C∞ manifolds, Parts I and II, Studia Math., 76 (1983), pp. 1-58; 95-136.
    • (1983) Studia Math. , vol.76 , pp. 1-58
    • Ciesielski, Z.1    Figiel, T.2
  • 10
  • 13
    • 0031069391 scopus 로고    scopus 로고
    • Stable multiscale bases and local error estimation for elliptic problems
    • S. DAHLKE, W. DAHMEN, R. HOCHMUTH, AND R. SCHNEIDER, Stable multiscale bases and local error estimation for elliptic problems, Appl. Numer. Math., 23 (1997), pp. 21-47.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 21-47
    • Dahlke, S.1    Dahmen, W.2    Hochmuth, R.3    Schneider, R.4
  • 14
    • 1842484444 scopus 로고    scopus 로고
    • Stability of multiscale transformations
    • W. DAHMEN, Stability of multiscale transformations, J. Fourier Anal. Appl., 2 (1996), pp. 341-361.
    • (1996) J. Fourier Anal. Appl. , vol.2 , pp. 341-361
    • Dahmen, W.1
  • 15
    • 0003081073 scopus 로고
    • Multiscale analysis, approximation, and interpolation spaces
    • C.K. Chui and L.L. Schumaker, eds., World Scientific, River Edge, NJ
    • W. DAHMEN, Multiscale analysis, approximation, and interpolation spaces, in Approximation Theory VIII, Wavelets and Multilevel Approximation, C.K. Chui and L.L. Schumaker, eds., World Scientific, River Edge, NJ, 1995, pp. 47-88.
    • (1995) Approximation Theory VIII, Wavelets and Multilevel Approximation , pp. 47-88
    • Dahmen, W.1
  • 16
    • 85011480386 scopus 로고    scopus 로고
    • Wavelet and multiscale methods for operator equations
    • Cambridge University Press, Cambridge, UK, 1197
    • W. DAHMEN, Wavelet and multiscale methods for operator equations, Acta Numer., 6 (1997), pp. 55-228, Cambridge University Press, Cambridge, UK, 1197.
    • (1997) Acta Numer. , vol.6 , pp. 55-228
    • Dahmen, W.1
  • 17
    • 33845592412 scopus 로고
    • Multilevel preconditioning
    • W. DAHMEN AND A. KUNOTH, Multilevel preconditioning, Numer. Math., 63 (1992), pp. 315-344.
    • (1992) Numer. Math. , vol.63 , pp. 315-344
    • Dahmen, W.1    Kunoth, A.2
  • 18
    • 0001787026 scopus 로고    scopus 로고
    • Biorthogonal spline wavelets on the interval stability and moment conditions
    • W. DAHMEN, A. KUNOTH, AND K. URBAN, Biorthogonal spline wavelets on the interval stability and moment conditions, Appl. Comput. Harmon. Anal., 6 (1999), pp. 132-196.
    • (1999) Appl. Comput. Harmon. Anal. , vol.6 , pp. 132-196
    • Dahmen, W.1    Kunoth, A.2    Urban, K.3
  • 20
    • 0000827236 scopus 로고
    • Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution
    • W. DAHMEN, S. PRÖSSDORF, AND R. SCHNEIDER, Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution, Adv. Comput. Math., 1 (1993), pp. 259-335.
    • (1993) Adv. Comput. Math. , vol.1 , pp. 259-335
    • Dahmen, W.1    Prössdorf, S.2    Schneider, R.3
  • 21
    • 0003224965 scopus 로고    scopus 로고
    • Composite wavelet bases for operator equations
    • in press
    • W. DAHMEN AND R. SCHNEIDER, Composite wavelet bases for operator equations, Math. Comp., in press.
    • Math. Comp.
    • Dahmen, W.1    Schneider, R.2
  • 22
    • 0000619262 scopus 로고    scopus 로고
    • Wavelets with complementary boundary conditions - function spaces on the cube
    • W. DAHMEN AND R. SCHNEIDER, Wavelets with complementary boundary conditions - function spaces on the cube, Results Math., 34 (1998), pp. 255-293.
    • (1998) Results Math. , vol.34 , pp. 255-293
    • Dahmen, W.1    Schneider, R.2
  • 24
    • 0000930347 scopus 로고    scopus 로고
    • Element-by-element construction of wavelets satisfying stability and moment conditions
    • W. DAHMEN AND R. STEVENSON, Element-by-element construction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal., 37 (1999), pp. 319-352.
    • (1999) SIAM J. Numer. Anal. , vol.37 , pp. 319-352
    • Dahmen, W.1    Stevenson, R.2
  • 25
    • 0001220724 scopus 로고
    • Compression of wavelet decompositions
    • R. A. DEVORE, B. JAWERTH, AND V. POPOV, Compression of wavelet decompositions, Amer. J. Math., 114 (1992), pp. 737-785.
    • (1992) Amer. J. Math. , vol.114 , pp. 737-785
    • Devore, R.A.1    Jawerth, B.2    Popov, V.3
  • 27
    • 0002712749 scopus 로고
    • Smooth parametric surfaces and n-sided patches
    • W Dahmen, M. Gasca, and C.A. Micchelli, eds., NATO ASI Series, Kluwer Academic Publishers, Dordrecht, the Netherlands
    • J. A. GREGORY, V. K. H. LAU, AND J. ZHOU, Smooth parametric surfaces and n-sided patches, in Computation of Curves and Surfaces, W Dahmen, M. Gasca, and C.A. Micchelli, eds., NATO ASI Series, Kluwer Academic Publishers, Dordrecht, the Netherlands, 1990.
    • (1990) Computation of Curves and Surfaces
    • Gregory, J.A.1    Lau, V.K.H.2    Zhou, J.3
  • 28
    • 21844511143 scopus 로고
    • Remarks on the abstract theory of additive and multiplicative Schwarz algorithms
    • M. GRIEBEL AND P. OSWALD, Remarks on the abstract theory of additive and multiplicative Schwarz algorithms, Numer. Math., 70 (1995), pp. 163-180.
    • (1995) Numer. Math. , vol.70 , pp. 163-180
    • Griebel, M.1    Oswald, P.2
  • 30
    • 0024607521 scopus 로고
    • Geometric continuous patch complexes
    • J. HAHN, Geometric continuous patch complexes, Comput. Aided Geom. Design, 6 (1989), pp. 55-67.
    • (1989) Comput. Aided Geom. Design , vol.6 , pp. 55-67
    • Hahn, J.1
  • 32
    • 0026909957 scopus 로고
    • Wavelet methods for fast resolution of elliptic problems
    • S. JAFFARD, Wavelet methods for fast resolution of elliptic problems, SIAM J. Numer. Anal., 29 (1992), pp. 965-986.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 965-986
    • Jaffard, S.1
  • 36
    • 0001594654 scopus 로고
    • Multilevel preconditioning-appending boundary conditions by Lagrange multipliers
    • A. KUNOTH, Multilevel preconditioning-appending boundary conditions by Lagrange multipliers, Adv. Comput. Math., 4 (1995), pp. 145-170.
    • (1995) Adv. Comput. Math. , vol.4 , pp. 145-170
    • Kunoth, A.1
  • 37
    • 0000423051 scopus 로고
    • Analyses, multi-résolutions nonorthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle
    • P. G. LEMARIÉ-RIEUSSET, Analyses, multi-résolutions nonorthogonales, commutation entre projecteurs et derivation et ondelettes vecteurs à divergence nulle, Rev. Mat. Iberoamericana, 8 (1992), pp. 221-237.
    • (1992) Rev. Mat. Iberoamericana , vol.8 , pp. 221-237
    • Lemarié-Rieusset, P.G.1
  • 38
    • 0003575867 scopus 로고
    • Non-Homogeneous Boundary Value Problems and Applications
    • Springer-Verlag, New York, Heidelberg
    • J. L. LIONS AND E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Grundlehren, Vol. 181, Springer-Verlag, New York, Heidelberg, 1973.
    • (1973) Grundlehren , vol.181
    • Lions, J.L.1    Magenes, E.2
  • 40
    • 84941836400 scopus 로고
    • Fictitious components and subdomain alternating methods
    • S. V. NEPOMNYASCHIKH, Fictitious components and subdomain alternating methods, Sov. J. Numer. Anal. Math. Model., 5 (1990), pp. 53-68.
    • (1990) Sov. J. Numer. Anal. Math. Model. , vol.5 , pp. 53-68
    • Nepomnyaschikh, S.V.1
  • 42
    • 0032342028 scopus 로고    scopus 로고
    • TURBS - topologically unrestricted rational B-splines
    • U. REIF, TURBS - topologically unrestricted rational B-splines, Constr. Approx., 14 (1998), pp. 57-77.
    • (1998) Constr. Approx. , vol.14 , pp. 57-77
    • Reif, U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.