To handle matrices with very large norms where the scaling and squaring procedure may not be efficient, the algorithm can be extended by incorporating adaptive strategies based on the matrix properties. One approach could be to implement a dynamic scaling mechanism that adjusts the scaling parameter based on the norm of the matrix. For matrices with large norms, the algorithm can switch to alternative methods that are more suitable for such cases, such as higher-order Taylor approximations or specialized Padé approximants designed for large values. By incorporating a mechanism to detect when the scaling and squaring procedure becomes inefficient, the algorithm can intelligently switch to more appropriate methods to ensure accurate computations for matrices with very large norms.