Abstract
Recent applications in science and engineering require a reliable implementation of the action of the matrix exponential and related φ functions. For possibly large matrices an approximation up to a certain tolerance needs to be obtained in a robust and efficient way. In this work we consider Leja interpolation for performing this task. Our focus lies on a new a posteriori error estimate for the method. We introduce the notion of a residual based estimate, where the residual is obtained from differential equations defining the φ functions. The properties of this new error estimate are investigated and compared to an existing one. Further, a numerical investigation is performed based on test examples originating from spatial discretization of time dependent partial differential equations in two and three space dimensions. The experiments show that this new approach is robust for various types of matrices and applications.
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