Gyurhan H. Nedzhibov†
Abstract: In this work, we develop a new and e cient iterative method for diagonalization of the Frobenius companion matrix. The method can be used for approximating all of the eigenvalues and corresponding eigenvectors. It can also be used for simultaneous inclusion of all simple zeros of the corresponding characteristic polynomial. Local convergence analysis of the method is included. We prove that it is locally quadratically convergent. Some numerical examples demonstrating effectiveness of the proposed iterative method are also included.
MSC: 65H04, 65H05, 65F15
keywords: Frobenius companion matrix, Eigen-decomposiotion, Iterative diagonalization, Polynomial zeros, Rayleigh quotient.
DOI 10.56082/annalsarscimath.2021.1-2.45
†g.nedzhibov@shu.bg Faculty of Mathematics and Informatics, Shumen University, Shumen 9700, Bulgaria; Paper written with nancial support of Shumen University under Grant RD 08-93/01.02.2019.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 13 no 1-2, 2021
