Fast transforms: Banded matrices with banded inverses
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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).
Date issued
2010-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
0027-8424
1091-6490