Optimized scaling and squaring for matrix functions appearing in exponential integrators

抄録

The study explores algorithms for evaluating matrix φ functions, focusing on the scaling and squaring method, which combines approximation formulas with double-angle relations. Despite its effectiveness, the method's optimal degree of the formula remains underexplored due to the computational burden of matrix multiplications within the relations. To address this, we propose an alternative method that achieves equivalence to these relations without the extensive use of matrix multiplications. Furthermore, we determine the optimum degree for the approximation formula.