Fast transforms: banded matrices with banded inverses. (English) Zbl 1205.65348
Summary: 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 \(A = F_{1}\cdots F_N\) 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).
MSC:
| 65T60 | Numerical methods for wavelets |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
| 15A09 | Theory of matrix inversion and generalized inverses |
References:
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