Department of Mathematics
Decay in functions of multiband matrices
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. © 2010 Society for Industrial and Applied Mathematics.
Banded matrices, Exponential decay, Matrix functions, Multiband matrices, Multilevel matrices, Numerical range, Polynomial approximation, Toeplitz matrices
Source Publication Title
SIAM Journal on Matrix Analysis and Applications
Society for Industrial and Applied Mathematics
Mastronardi, N., M. Ng, and E. E. Tyrtyshnikov. "Decay in functions of multiband matrices." SIAM Journal on Matrix Analysis and Applications 3.5 (2010): 2721-2737.