The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Fast wavelet transforms and numerical algorithms I
Abstract
A class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors. Previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices. In contrast, the methods presented here are based on the recently developed theory of wavelets and are applicable to all Calderon‐Zygmund and pseudo‐differential operators. The algorithms of this paper require order O(N) or O(N log N) operations to apply an N × N matrix to a vector (depending on the particular operator and the version of the algorithm being used), and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here.
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Citations
Cites
Orthonormal bases of compactly supported wavelets
Daubechies, I. (1988) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160410705 · Cited by 8,190
A fast algorithm for particle simulations
Greengard, L., & Rokhlin, V (1987) · Journal of Computational Physics · doi:10.1016/0021-9991(87)90140-9 · Cited by 4,868
Self-citationMeyer, Y. (1993) · Cambridge University Press eBooks · doi:10.1017/cbo9780511623820 · Cited by 2,034
Multifrequency channel decompositions of images and wavelet models
Mallat, S. G. (1989) · IEEE Transactions on Acoustics, Speech, and Signal Processing · doi:10.1109/29.45554 · Cited by 1,955
A Fast Adaptive Multipole Algorithm for Particle Simulations
Carrier, J., Greengard, L., & Rokhlin, V. (1988) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0909044 · Cited by 617
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Cited by
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.
Daubechies, I., Defrise, M., & De Mol, C. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20042 · Cited by 4,958
Fast Discrete Curvelet Transforms
Candès, E., Demanet, L., Donoho, D., & Ying, L. (2006) · Multiscale Modeling & Simulation · doi:10.1137/05064182x · Cited by 2,573
Multiresolution analysis for surfaces of arbitrary topological type
Lounsbery, M., DeRose, T. D., & Warren, J. (1997) · ACM Transactions on Graphics · doi:10.1145/237748.237750 · Cited by 760
Boehm, K. M., Aherne, E. A., Ellenson, L., Nikolovski, I., Alghamdi, M., Vázquez-García, I., Zamarin, D., Long Roche, K., Liu, Y., Patel, D., et al. (2022) · Nature Cancer · doi:10.1038/s43018-022-00388-9 · Cited by 357
Metadata
- Authors
- Beylkin, G., Coifman, R., & Rokhlin, V.
- Venue
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Published
- 1991-03
- Volume
- 44
- Issue
- 2
- Pages
- 141-183
- ISSN
- 0010-3640 (ISSN-L)
- 1097-0312
- OpenAlex
- W2094585768
- Cited by
- 1,770
- References
- 5
- FWCI
- 89.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Beylkin, G., Coifman, R., & Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms I. Communications on Pure and Applied Mathematics. https://doi.org/10.1002/cpa.3160440202
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