
06361433
j
2014f.00699
Jain, Nitin A.
Murthy, Kushal D.
Hamsapriye
Matrix methods for finding $\root n \of {m^u}$.
Int. J. Math. Educ. Sci. Technol. 45, No. 5, 754762 (2014).
2014
Taylor \& Francis, Abingdon, Oxfordshire
EN
H65
N55
diagonalization
$n$th roots of unity
linearly independent eigenvectors
spanning space
autocorrelation
convolution
doi:10.1080/0020739X.2013.877607
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.