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Advances in Computational Mathematics

Volumn 1, Issue 3, 1993, Pages 259-335

Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution

(3) Dahmen, W a Prossdorf S b Schneider, R c

a RWTH AACHEN UNIVERSITY (Germany)

b LEIBNIZ INSTITUT FÜR KATALYSE E V AN DER UNIVERSITÄT ROSTOCK (Germany)

c DARMSTADT UNIVERSITY OF TECHNOLOGY (Germany)

Author keywords

atomic decomposition; biorthogonal wavelets; Calder n Zygmund operators; error analysis; generalized Petrov Galerkin schemes; matrix compression; Periodic pseudodifferential equations; pre wavelets; Subject classification AMS: 65F35, 65J10, 65N30, 65N35, 65R20, 47A20, 47G30, 45P05, 41A25; wavelet representation

Indexed keywords

EID: 0000827236 PISSN: 10197168 EISSN: 15729044 Source Type: Journal
DOI: 10.1007/BF02072014 Document Type: Article

Times cited : (162)

References (42)

1
- 84936220168
- B. Alpert, Sparse representation of smooth linear operators, Preprint, PhD Thesis, Yale University (1990).

2
- 84936191944
- B. Alpert, G. Beylkin, R. Coifman and V. Rokhlin, Wavelets for the fast solution of second-kind integral equations, Preprint, Yale University (1990).

3
- 0038976118
- On elliptic pseudodifferential operators on a closed curve
- (1985) Trans. Moscow Math. Soc. , vol.47 , pp. 23-74
- Agranovich, M.S.¹

4
- 84990610636
- The fast wavelet transform and numerical algorithms
- (1991) Communications on Pure and Applied Mathematics , vol.44 , pp. 141-183
- Beylkin, G.¹ Coifman, R.² Rokhlin, V.³

5
- 0026995365
- On the representation of operators in bases of compactly supported wavelets
- (1992) SIAM J. Numer. Anal. , vol.29 , pp. 1716-1740
- Beylkin, G.¹

6
- 28144464582
- Multilevel matrix multiplication and fast solution of integral equations
- (1991) J. Comp. Phys. , vol.90 , pp. 348-370
- Brandt, A.¹ Lubrecht, A.A.²

7
- 84936171113
- A.S. Cavaretta, W. Dahmen and CA. Micchelli, Stationary subdivision, Memoirs Amer. Math. Soc. 93, no. 453 (1991).

8
- 84936196928
- C.K. Chui, An Introduction to Wavelets, Vol. 1 (Academic Press, 1992).

9
- 84936192037
- C.K. Chui, J. Stöckler and J.D. Ward, Compactly supported box spline wavelets, Technical Report, Preprint (1990).

10
- 84990623513
- Biorthogonal bases of compactly supported wavelets
- (1992) Communications on Pure and Applied Mathematics , vol.45 , pp. 485-560
- Cohen, A.¹ Daubechies, I.² Feauveau, J.-C.³

11
- 84936206897
- R. Coifman and Y. Meyer, Au-delá des opérateur pseudo-différentiels, Astérisque no. 57, Société Math. de France (1978).

12
- 84936206846
- W. Dahmen, Locally finite decompositions of nested spaces and applications to operator equations, in: Algorithms for Approximation, ed. M.G. Cox and J.C. Mason, to appear.

13
- 33845592412
- Multilevel preconditioning
- (1992) Numer. Math. , vol.63 , pp. 315-345
- Dahmen, W.¹ Kunoth, A.²

14
- 84936215774
- W. Dahmen and C.A. Micchelli, Recent progress in multivariate splines, in: Approximation Theory IV, ed. C.K. Chui, L.L. Schumaker and J.D. Ward (Academic Press, 1983) pp. 27–121.

15
- 84936179868
- W. Dahmen and C.A. Micchelli, Biorthogonal wavelet expansions, in preparation.

16
- 0027574359
- Using the refinement equation for the evaluation of integrals of wavelets
- (1993) SIAM J. Numer. Anal. , vol.30 , pp. 507-537
- Dahmen, W.¹ Micchelli, C.A.²

17
- 84936215463
- W. Dahmen, S. Prössdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations I: Stability and convergence, Preprint, Institut für Angewandte Analysis und Stochastik no. 7 (1992), to appear in Math. Zeits.

18
- 84990575058
- Orthonormal bases of compactly supported wavelets
- (1988) Communications on Pure and Applied Mathematics , vol.41 , pp. 909-996
- Daubechies, I.¹

19
- 84936206902
- I. Daubechies, Ten Lectures on Wavelets, CBMS-NDF Regional Conf. Series in Appl. Math. 61 (1992).

20
- 84936182220
- G. David, Wavelets and Singular Integrals on Curves and Surfaces, Lecture Notes in Math. 1465 (Springer, 1991).

21
- 0001720260
- A boundedness criterion for generalized Calderón-Zygmund operators
- (1984) The Annals of Mathematics , vol.120 , pp. 371-397
- David, G.¹ Journée, J.-L.²

22
- 84936202582
- R. DeVore, B. Jawerth and V. Popov, Compression of wavelet decompositions, Technical Report, Preprint (1990).

23
- 84966241361
- Interpolation of Besov spaces
- (1988) Transactions of the American Mathematical Society , vol.305 , pp. 397-414
- DeVore, R.¹ Popov, V.²

24
- 0001617415
- On the fast matrix multiplication in the boundary element method by panel clustering
- (1989) Numer. Math. , vol.54 , pp. 463-491
- Hackbusch, W.¹ Nowak, Z.P.²

25
- 84936182434
- A. Harten and I. Yad-Shalom, Fast multiresolution algorithm for matrix-vector multiplications, ICASE Report No. 92-55 (1992).

26
- 0003668851
- Springer, Berlin/Heidelberg/New York/Tokyo
- (1985) The Analysis of Linear Partial Differential Operators, Vol. 1–4, Grundlehren
- Hörmander, L.¹

27
- 0002888350
- Using the refinement equation for the construction of pre-wavelets II: Power of two
- P., Laurent, A., Le Méhauté, L.L., Schumaker, Academic Press, New York
- (1991) Curves and Surfaces , pp. 204-246
- Jia, R.Q.¹ Micchelli, C.A.²

28
- 0004276194
- MIT Press, Boston
- (1981) Pseudodifferential Operators
- Kumano-go, H.¹

29
- 84966210236
- Multiresolution approximation and wavelet orthonormal bases of L²
- (1989) Trans. Amer. Math. Soc. , vol.315 , pp. 69-87
- Mallat, S.¹

30
- 84985351746
- Local and global description of periodic pseudodifferential operators
- (1991) Mathematische Nachrichten , vol.150 , pp. 151-161
- McLean, W.¹

31
- 84933843727
- University of New South Wales, Australia
- (1989) Periodic pseudodifferential operators and periodic function spaces
- McLean, W.¹

32
- 84936179122
- Y. Meyer, Wavelets and Operators, Proc. special year in modern analysis, Urbana (1986/87).

33
- 0004180195
- Hermann, Paris
- (1990) Ondelettes et Opérateurs 1: Ondelettes
- Meyer, Y.¹

34
- 0004180195
- Hermann, Paris
- (1990) Ondelettes et Opérateurs 2: Opérateur de Calderón-Zygmund
- Meyer, Y.¹

35
- 0041146999
- Spline approximation methods for multidimensional periodic pseudodifferential equations
- (1992) Integral Equations and Operator Theory , vol.15 , pp. 626-672
- Prössdorf, S.¹ Schneider, R.²

36
- 84936170240
- S. Prössdorf and R. Schneider, Pseudodifferential operators — A symbolic calculus for approximation methods for periodic pseudodifferential equations, TH-Fb Math. Preprint (1991).

37
- 84936169099
- S. Riemenschneider and Z. Shen, Wavelets and pre-wavelets in low dimensions, Technical Report, Preprint (1991).

38
- 0003738691
- M.B., Ruskai, et al., Jones and Barlett, Boston
- (1992) Wavelets and Their Applications
- Ruskai, M.B.¹

39
- 84985338005
- On ɛ-collocation for pseudodifferential equations on close curves
- (1986) Mathematische Nachrichten , vol.126 , pp. 183-196
- Schmidt, G.¹

40
- 0003547220
- Springer, Berlin
- (1985) Pseudodifferential Operators and Spectral Theory
- Shubin, M.A.¹

41
- 0003799686
- Princeton University Press, Princeton, NJ
- (1970) Singular Integrals and Differentiability Properties of Functions
- Stein, E.M.¹

42
- 0004276192
- Princeton University Press, Princeton, NJ
- (1981) Pseudodifferential Operators
- Taylor, M.¹

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