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, Page 524-528 PDF (439.09 K) | ||||
Document Type: Original Article | ||||
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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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