Fatoorehchi, H., Abolghasemi, H. (2014). Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method. test, 22(3), 524-528.
Hooman Fatoorehchi; Hossein Abolghasemi. "Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method". test, 22, 3, 2014, 524-528.
Fatoorehchi, H., Abolghasemi, H. (2014). 'Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method', test, 22(3), pp. 524-528.
Fatoorehchi, H., Abolghasemi, H. Finding all real roots of a polynomial by matrix algebra and the Adomian decomposition method. test, 2014; 22(3): 524-528.

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

Journal of the Egyptian Mathematical Society
Volume 22, Issue 3, October 2014, Pages 524-528    PDF (439.09 K)
Document Type: Original Article
Authors
Hooman Fatoorehchi1; Hossein Abolghasemi2
1Center for Separation Processes Modeling and Nano-Computations, School of Chemical Engineering, College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran
2Oil 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
Polynomial zeroes; Adomian decomposition method; Adomian polynomials; Matrix algebra; Gershgorin’s theorem; Eigenvalue
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