Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method

Document Type : Original Article

Authors

1 Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

2 Oil and Gas Center of Excellence, University of Tehran, Tehran, Iran

Abstract

In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial
equation through the Adomian decomposition method equipped with a number of developed
theorems from matrix algebra. These auxiliary theorems are associated with eigenvalues of
matrices and enable convergence of the Adomian decomposition method toward different real roots of the target polynomial equation. To further improve the computational speed of our technique, a nonlinear convergence accelerator known as the Shanks transform has optionally been employed. For the sake of illustration, a number of numerical examples are given.

Keywords

Journal of the Egyptian Mathematical Society
Volume 22, Issue 3 - Serial Number 3
October 2014
Pages 524-528

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