Decay bounds for functions of matrices with banded or Kronecker structure

Abstract

We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture the actual (non-monotonic) decay behavior of the entries of functions of matrices with Kronecker sum structure. We also discuss extensions to more general sparse matrices.

References in corpus (2)

• An Exact Formulation of the Time-Ordered Exponential using Path-Sums
• Localized spectrum slicing

Cited by in corpus (4)

• Analytic functional calculus for two operators
• Local Exponential Methods: a domain decomposition approach to exponential time integration of PDEs
• Approximation of functions of large matrices with Kronecker structure
• Sparse solution of the Lyapunov equation for large-scale interconnected systems