The algorithm can be further optimized for specific use cases by incorporating tailored strategies to preserve the Lie group structure or avoid matrix inversions. Some optimization techniques include:
Lie Group Preservation: For applications where preserving the Lie group structure is essential, the algorithm can prioritize the use of diagonal Padé approximants that exactly preserve the Lie group properties. By incorporating additional constraints or penalties in the method selection process, the algorithm can ensure the preservation of the Lie group structure while maintaining computational efficiency.
Avoiding Matrix Inversions: To optimize the algorithm for cases where matrix inversions are to be avoided, the selection criteria can be modified to exclude methods that involve matrix inversions. By prioritizing methods that do not require inversions or by penalizing methods with inversion steps, the algorithm can be tailored to specific use cases where matrix inversions are undesirable.