A Krylov subspace method for the approximation of bivariate matrix functions
Provides a unified framework and new convergence insights for numerical linear algebra problems involving bivariate matrix functions.
The authors propose a tensorized Krylov subspace method for approximating bivariate matrix functions and provide convergence analysis, yielding new estimates for most instances except Sylvester equations.
Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fréchet derivative. In this work, we propose a novel tensorized Krylov subspace method for approximating such bivariate matrix functions and analyze its convergence. While this method is already known for some instances, our analysis appears to result in new convergence estimates and insights for all but one instance, Sylvester matrix equations.