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Tisseur, F. (2001) Newton’s Method in Floating Point Arithmetic and Iterative Refinement of Generalized Eigenvalue Problems. SIAM Journal on Matrix Analysis and Applications, 22, 1038-1057.
https://doi.org/10.1137/S0895479899359837

has been cited by the following article:

• 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.