Verified computation of real powers of matrices

Two numerical algorithms based on verified block diagonalization (VBD) are proposed to compute interval matrices containing the matrix real powers. The first algorithm uses VBD based on numerical spectral decomposition involving cubic complexity if the power exponent’s absolute value is not too large. In contrast, the second algorithm adopts VBD based on numerical Jordan decomposition involving quartic complexity, which is applicable even for defective matrices. Numerical results show the effectiveness of the algorithms.