Fast transforms: Banded matrices with banded inverses
Gilbert Strang (MIT)

The success of wavelets depends on the property that the inverse wavelet transform also involves finite length filters.  So the transform and its inverse are both represented by **banded matrices**.  We provide a new factorization for all matrices (most of them far from wavelets!) with this exceptional property.  A combinatorial question about permutation matrices (banded of course) will also arise.