Author(s)

R. O. Akinola^*, K. Musa, I. A. Nyam, S. Y. Kutchin, K. V. Joshua

Department of Mathematics, Faculty of Natural Sciences, University of Jos, Jos, Nigeria.

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.

Quadratic Convergence, Newton’s Method

Akinola, R. , Musa, K. , Nyam, I. , Kutchin, S. and Joshua, K. (2017) An Efficient Algorithm for the Numerical Computation of the Complex Eigenpair of a Matrix. Journal of Applied Mathematics and Physics, 5, 680-692. doi: 10.4236/jamp.2017.53057.