RESUMEN
A new iterative scheme has been constructed for finding minimal solution of a rational matrix equation of the form X + A*X (-1) A = I. The new method is inversion-free per computing step. The convergence of the method has been studied and tested via numerical experiments.
Asunto(s)
Algoritmos , Modelos TeóricosRESUMEN
We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.