Decay in Functions of Multiband Matrices
Nicola Mastronardi, M. Ng, E. E. Tyrtyshnikov · SIAM Journal on Matrix Analysis and Applications · 2010
The Benzi–Golub result on decay properties for matrix functions of a banded Hermitian matrix [BIT, 39 (1999), pp. 417–438] is extended to the case of multiband matrices. It is shown how the simple diagonal dominance technique applies to the general non-Hermitian case. We also present $O(1)$ algorithms computing matrix functions of multiband and multi-Toeplitz (multilevel Toeplitz) matrices in time that depends on the bandwidth and prescribed approximation accuracy but does not depend on the size of matrices.