On monotonicity of the Lanczos approximation to the matrix exponential
The spectral Lanczos decomposition method is applied to the computation of \(u(t) = \exp(At)\varphi\), where \(A\) is a symmetric matrix and \(\varphi\) is a given unit vector. The results are applicable in exact arithmetic only since they use the minimal polynomial of \(\varphi\) relative to \(A\) which can be destroyed in the presence of rounding errors.
scientific article; zbMATH DE number 5349141