Fast transforms: Banded matrices with banded inverses
نویسندگان
چکیده
منابع مشابه
Fast transforms: Banded matrices with banded inverses.
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 gr...
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AproductADF1 : : : FN of invertible block-diagonalmatrices will be bandedwith a banded inverse. We establish this factorization with the numberN controlled by the bandwidthsw and not by the matrix size n:When A is an orthogonal matrix, or a permutation, or banded plus finite rank, the factors Fi have w D 1 and generate that corresponding group. In the case of infinite matrices, conjectures rema...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2010
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.1005493107