A Rational Interpolation Technique To Approximate The Time- Dependent Matrix Exponential

While the computation of the matrix exponential is known to be dubious, the computed value is used widely in system analysis. This is especially true for the time-dependent matrix exponential. As the systems that we model become more complex, the order of the systems, and thus the order of the matrix exponential become larger. Even with today’s increases in processing power, the computation of numerous values to visualize or analyze the system can tax computational output to point where a degradation in performance can be seen by the user. Often great accuracy is not needed especially in the visualization and interpolations can be used. In this paper, we present a rational interpolation method to estimate the time-dependent matrix exponential that can also estimate the error bound of the interpolation. We clearly note that, while this method utilizes significantly less computational resources than actual computation, it is dependent on the actual computational method chosen for its performance.