Using Krylov approximations to the matrix exponential operator in Davidsonʹs method Original Research Article

This paper presents a new look at Davidsonʹs method for the calculation of the rightmost eigenvalue(s). The combination of time-stepping by the Krylov exponential propagator and the Davidson method leads to a method that builds a Krylov space of the matrix exponential. The method is well-suited when only a matrix–vector multiplication by A is possible. The paper presents some convergence results and numerical examples, including a comparison with the Jacobi–Davidson method.