Fast transforms: Banded matrices with banded inverses.
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- Record sourced from PubMed, PMID 20615937.
- Also identified by DOI 10.1073/pnas.1005493107 and PMC identifier 2906572.
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Abstract
It is unusual for both A and A(-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(1)...F(N) where N is controlled by the bandwidths of A and A(-1) (but not by their size, so this extends to infinite matrices and leads to new matrix groups).
Medical subject headings
- Mathematical Concepts