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

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

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In this paper, we put forth a combined method for calculation of all real zeroes of a polynomial equation through amino acid 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 Collections 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.