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).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Proceedings of the National Academy of Sciences
National Academy of Sciences (U.S.)
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.
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