TITLE:
An Efficient Algorithm for the Numerical Computation of the Complex Eigenpair of a Matrix
AUTHORS:
R. O. Akinola, K. Musa, I. A. Nyam, S. Y. Kutchin, K. V. Joshua
KEYWORDS:
Quadratic Convergence, Newton’s Method
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.3,
March
24,
2017
ABSTRACT: In computing the desired complex eigenpair of a matrix, we show that by adding Ruhe’s normalization to the matrix pencil, we obtain a square nonlinear system of equations. In this work, we show that the corresponding Jacobian is non-singular at the root and that with an appropriately chosen initial guesses, Ruhe’s normalization with a fixed complex vector not only converges quadratically but also faster than the earlier Algorithms for the numerical computation of the complex eigenpair of a matrix. The mathematical tools used in this work are Newton and Gauss-Newton’s methods.