Wavelets with patchwise cancellation properties

Mathematics of Computation

Volumn 75, Issue 256, 2006, Pages 1871-1889

  Harbrecht, Helmut ^a   Stevenson, R O B ^b  

^a UNIVERSITY OF KIEL   (Germany)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Domain decomposition; Matrix compression; Patchwise cancellation properties; Riesz bases; Wavelets

Indexed keywords

EID: 33750882679     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-06-01867-9     Document Type: Article

References (22)

1. [BF01] S. Bertoluzza and S. Falletta. Wavelets on ]0,1[at large scales. Pubbl. 1212, I.A.N. Pavia, 2001.
2. [CDD01] A. Cohen, W. Dahmen, and R. DeVore. Adaptive wavelet methods for elliptic operator equations - Convergence rates. Math. Comp, 70:27-75, 2001. MR1803124 (2002h:65201)
3. [CDD02] A. Cohen, W. Dahmen, and R. DeVore. Adaptive wavelet methods II - Beyond the elliptic case. Found. Comput. Math., 2(3):203-245, 2002. MR1907380 (2003f:65212)
4. [CDF92] A. Cohen, I. Daubechies, and J.C. Feauveau. Biorthogonal bases of compactly supported wavelets. Comm. Pur. Appl. Math., 45:485-560, 1992. MR1162365 (93e:42044)
5. [CDP96] J.M. Carnicer, W. Dahmen, and J.M. Peña. Local decomposition of refinable spaces and wavelets. Appl. and Comp. Harm. Anal., 3:127-153, 1996. MR1385049 (97f:42050)
6. [CM00] A. Cohen and R. Masson. Wavelet adaptive method for second order elliptic problems: Boundary conditions and domain decomposition. Numer. Math., 86:193-238, 2000. MR1777487 (2001j:65185)
7. [CTU99] C. Canuto, A. Tabacco, and K. Urban. The wavelet element method part I: Construction and analysis. Appl. Comput. Harmon. Anal., 6:1-52, 1999. MR1664902 (99k:42055)
8. [DHS02] W. Dahmen, H. Harbrecht, and R. Schneider. Compression techniques for boundary integral equations - optimal complexity estimates. SIAM J. Numer. Anal., 43(6):2251-2271, 2006. MR2206435
9. [DKU99] W. Dahmen, A. Kunoth, and K. Urban. Biorthogonal spline-wavelets on the interval - stability and moment conditions. Appl. Comp. Harm. Anal., 6:132-196, 1999. MR1676771 (99m:42046)
10. [DS98] W. Dahmen and R. Schneider. Wavelets with complementary boundary conditions - function spaces on the cube. Results Math., 34(3-4):255-293, 1998. MR1652724 (99h:42057)
11. [DS99a] W. Dahmen and R. Schneider. Composite wavelet bases for operator equations. Math. Comp., 68:1533-1567, 1999. MR1648379 (99m:65122)
12. [DS99b] W. Dahmen and R. Schneider. Wavelets on manifolds I: Construction and domain decomposition. SIAM J. Math. Anal., 31:184-230, 1999. MR1742299 (2000k:65242)
13. [GS04] T. Gantumur and R.P. Stevenson. Computation of differential operators in wavelet coordinates. Math. Comp., 75:697-709, 2006.
14. [GS05] T. Gantumur and R.P. Stevenson. Computation of singular integral operators in wavelet coordinates. Computing, 76:77-107, 2006. MR2174673
15. [Har01] H. Harbrecht. Wavelet Galerkin schemes for the boundary element method in three dimensions. Ph.D. Thesis, Technische Universität Chemnitz, Germany, 2001.
16. [HS04] H. Harbrecht and R. Schneider. Biorthogonal wavelet bases for the boundary element method, Math. Nachr. 269-270:167-188, 2004. MR2074780 (2005g:42080)
17. [KS04] A. Kunoth and J. Sahner. Wavelets on manifolds: An optimized construction. SFB 611 Preprint 163, Universität Bonn, July 2004.
18. To appear in Math. Comp.
19. [Sch98] R. Schneider. Multiskalen- und Wavelet-Matrixkompression: Analysisbasierte Methoden zur Lösung großer vollbesetzter Gleigungssysteme. Habilitationsschrift, 1995. Advances in Numerical Mathematics. Teubner, Stuttgart, 1998.
20. [Ste04a] R.P. Stevenson. Composite wavelet bases with extended stability and cancellation properties. Technical Report 1304, Utrecht University, July 2004.
21. To appear in in SIAM J. Numer. Anal.
22. [Ste04b] R.P. Stevenson. On the compressibility of operators in wavelet coordinates. SIAM J. Math. Anal., 35(5):1110-1132, 2004. MR2050194 (2005e:42128)