It is well known that the application of the homotopy analysis method (HAM) to
various problems can determine the valid region of the convergence-control parameter ~, either
by plotting the so-called ~-curve, or by minimizing the residual error. In this paper, we present
a new approach based on the spectral radius of the coefficient matrix to obtain a proper value
of ~, when the HAM is applied to systems of linear equations. We also present a detailed
discussion about the convergence of the HAM, and give a necessary and sufficient condition for
the obtained results, when the HAM is used for solving a system of linear equations.
کلید واژگان :
Homotopy Analysis Method, Homotopy Perturbation Method, System of Linear Equations, Convergence-Control Parameter.
