Fast transforms: Banded matrices with banded inverses
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Strang_Fast transforms.pdf
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497.75 KB
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Checksum (MD5)
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Author(s)
Strang, Gilbert
Date Issued
June 2010
Journal
Proceedings of the National Academy of Sciences
Publisher
National Academy of Sciences (U.S.)
Citation
Strang, G. “Inaugural Article: Fast transforms: Banded matrices with banded inverses.” Proceedings of the National Academy of Sciences 107, no. 28 (July 13, 2010): 12413-12416.
Version
Final published version
Abstract
It is unusual for both A and A[superscript -1] to be banded—but this can be a valuable property in applications. Block-diagonal matrices F are the simplest examples; wavelet transforms are more subtle. We show that every example can be factored into A = F[subscript 1]…F[subscript N] where N is controlled by the bandwidths of A and A[superscript -1} (but not by their size, so this extends to infinite matrices and leads to new matrix groups).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1073/pnas.1005493107
