Abstract
This paper presents a new look at Davidson's 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.
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