On monotonicity of the Lanczos approximation to the matrix exponential

Abstract

We prove strictly monotonic error decrease in the Euclidian norm of the Krylov subspace approximation of exp (A) φ, where φ and A are respectively a vector and a symmetric matrix. In addition, we show that the norm of the approximate solution grows strictly monotonically with the subspace dimension. © 2008 Elsevier Inc. All rights reserved.