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 groups).
Strang
Gilbert
G
Massachusetts Institute of Technology, Cambridge, MA 02139, USA. gs@math.mit.edu
D005583:Fourier Analysis; D055641:Mathematical Concepts