A self-validating numerical method for the matrix exponential (Q1262083)

An algorithm is presented which produces highly accurate and automatically verified bounds for \(\exp (A)=\sum^{\infty}_{k=0}A^ k/k!\) where A is a real \(n\times n\) matrix. The method is based on interval analysis techniques and the iterative defect correction principle. The ``scaling and squaring'' approach is realized by the Padé approximations and safe error monitoring. Finally there are three examples \((n=2\), \(n=3)\) in order to compare the numerical results with the results by conventional floating-point computations.