Author

M. Schweitzer

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Preprint Oct 2026

On the stability of basis construction in extended Krylov subspace methods

Extended Krylov subspace methods (EKSMs) are a well known approach for approximating the action of a matrix function on a vector $f(A)\mathbf{b}$, and their block versions are often used for solving Lyapunov and Sylvester matrix equations. EKSMs produce Laurent approximations to the underlying operator, which are gener...

Kathryn Lund, M. Schweitzer · 0 citations

Preprint Jul 2026

Field-of-values analysis of augmented Krylov methods for matrix $\varphi$-function actions

We revisit established Krylov subspace methods for linear combinations of matrix $\varphi$-function actions from the viewpoint of the block triangular formulation of Al-Mohy and Liu [SIAM J. Sci. Comput., 48 (2026), pp. A726--A747]. In algorithms such as KIOPS [J. Comput. Phys., 372 (2018), pp. 236--255], one uses an a...

Xiaobo Liu, M. Schweitzer · 0 citations