فهرست نشریات علمی دسترسی آزاد ایران

‎This paper introduces a verified interval iterative method for computing the principal $p$th root of a square matrix along with rigorous interval enclosures‎. ‎Leveraging the epsilon inflation technique‎, ‎the proposed algorithm is reformulated as an inclusion method‎, ‎enabling robust control over approximation and rounding errors in finite-precision arithmetic‎. ‎The method exhibits quadratic convergence and does not require an initial enclosure containing the exact root‎, ‎which is a common limitation in existing interval approaches‎. ‎We further demonstrate that the midpoint matrix sequence generated by the iteration is well-behaved and numerically stable‎. ‎Theoretical analysis confirms the convergence of the interval enclosures to the exact matrix root‎, ‎and numerical experiments validate the method’s efficiency for large-scale matrices and high values of $p$‎. ‎As a practical contribution‎, ‎we provide implementable Mathematica code for the proposed algorithm‎, ‎facilitating reproducibility and further exploration‎.