Open AccessFinding all real roots of a polynomial by matrix algebra and the Adomian decomposition method
Author(s) -
Hooman Fatoorehchi,
Hossein Abolghasemi
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.12.018
Subject(s) - adomian decomposition method , mathematics , convergence (economics) , eigenvalues and eigenvectors , polynomial , decomposition , matrix (chemical analysis) , eigendecomposition of a matrix , algebra over a field , matrix polynomial , decomposition method (queueing theory) , polynomial matrix , nonlinear system , mathematical analysis , pure mathematics , discrete mathematics , differential equation , ecology , physics , materials science , quantum mechanics , economics , composite material , biology , economic growth
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