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Matrix methods for finding \$\root n \of {m^u}\$. (English)
Int. J. Math. Educ. Sci. Technol. 45, No. 5, 754-762 (2014).
Summary: An iterative algorithm for finding \$\root n \of {m^u}\$, (\$m > 0\$, \$u < n\$), is developed which involves generating a sequence of approximations to \$\root n \of {m^u}\$ using the concept of eigenvectors. The convergence of this method is then established by studying the eigenvalues and eigenvectors of a matrix \$A_{n}\$, directly related to the algorithm itself. The matrix \$A_{n}\$ is constructed using the eigenvalues and eigenvectors, applying the concepts of diagonalization. An algorithm for finding higher powers of \$A_{n}\$ is explained. Using these higher powers of \$A_{n}\$, a direct method is also derived. Two numerical examples explaining the methods are given.
Classification: H65 N55