# Convergence and Stability of a New Parametric Class of Iterative Processes for Nonlinear Systems
## 5 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Iterative Method** & \(k\) & \(\rho\) & \(\epsilon_{approx}\) & \(\epsilon_{f}\) & \(\bar{\xi}\) & **Cpu-Time** \\ \hline \(ACTV^{6},\alpha=1\) & 4 & 6.0038 & \(8.580\times 10^{-76}\) & 0 & \(\xi_{1}\) & 3.5022 \\ \(ACTV^{6},\alpha=-5\) & 4 & 6.0001 & \(8.576\times 10^{-110}\) & 0 & \(\xi_{1}\) & 3.5053 \\ \(ACTV^{6},\alpha=-73.25\) & 4 & 5.883 & \(1.015\times 10^{-38}\) & \(1.299\times 10^{-7229}\) & \(\xi_{1}\) & 3.8991 \\ \(ACTV^{6},\alpha=-76.89\) & 4 & 5.874 & \(6.0584\times 10^{-38}\) & \(6.1856\times 10^{-225}\) & \(\xi_{1}\) & 3.4959 \\ Newton & 9 & 2.0000 & \(7.299\times 10^{-146}\) & \(1.964\times 10^{-291}\) & \(\xi_{1}\) & 1.2855 \\ C6\({}_{1}\) & 4 & 6.0011 & \(3.393\times 10^{-101}\) & 0 & \(\xi_{1}\) & 1.6573 \\ C6\({}_{2}\) & 4 & 6.0011 & \(1.044\times 10^{-88}\) & 0 & \(\xi_{1}\) & 1.5505 \\ \(B6,b_{1}=-3/5\) & 4 & 6.004 & \(2.675\times 10^{-75}\) & 0 & \(\xi_{1}\) & 1.7605 \\ \(B6,b_{1}=1\) & 4 & 6.0008 & \(6.720\times 10^{-92}\) & 0 & \(\xi_{1}\) & 1.5495 \\ \(PSH6,\alpha=0\) & 4 & 6.0101 & \(3.503\times 10^{-65}\) & 0 & \(\xi_{1}\) & 3.6422 \\ \(PSH6,\alpha=10\) & 4 & 6.0000 & \(1.013\times 10^{-125}\) & 0 & \(\xi_{1}\) & 3.5589 \\ \(PSH62,\alpha=10\) & 4 & 6.159 & \(2.556\times 10^{-34}\) & \(8.874\times 10^{-203}\) & \(\xi_{1}\) & 3.9764 \\ \(XH6\) & 4 & 6.0026 & \(1.161\times 10^{-80}\) & 0 & \(\xi_{1}\) & 1.6411 \\ \hline \end{tabular}
\end{table} 
Table 2: Results for function \(F_{1}\), using as seed \(x^{(0)}=(2.5,\ -1.5)\). \begin{table}
\begin{tabular}{c c c c c c} \hline
**Iterative Method** & \(k\) & \(\rho\) & \(\epsilon_{aprox}\) & \(\epsilon_{f}\) & \(\xi\) & **Cpu-Time** \\ \hline \(ACTV^{6},\alpha=1\) & 10 & 5.9096 & \(1.148\times 10^{-35}\) & \(4.953\times 10^{-211}\) & \(\xi_{1}\) & 8.2697 \\ \(ACTV^{6},\alpha=-5\) & 79 & 6.0503 & \(1.697\times 10^{-177}\) & 0 & \(\xi_{1}\) & 65.9107 \\ \(ACTV^{6},\alpha=-73.25\) & - & - & - & - & - \\ \(ACTV^{6},\alpha=-76.89\) & - & - & - & - & - \\ Newton & - & - & - & - & - \\ \(C6_{1}\) & - & - & - & - & - \\ \(C6_{2}\) & - & - & - & - & - \\ \(B6,b_{1}=-3/5\) & 6 & 5.9119 & \(1.353\times 10^{-35}\) & \(2.050\times 10^{-210}\) & \(\xi_{1}\) & 2.4022 \\ \(B6,b_{1}=1\) & - & - & - & - & - \\ \(PSH6_{1},\alpha=0\) & - & - & - & - & - \\ \(PSH6_{2},\alpha=10\) & 26 & 5.994 & \(7.5229\times 10^{-84}\) & 0 & \(\xi_{1}\) & 26.0787 \\ \(XH6\) & - & - & - & - & - \\ \hline \end{tabular}
\end{table} 
Table 4: Results for function \(F_{3}\) and initial guess \(x^{(0)}=(-17.76,\ -17.78)\). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Iterative Method** & \(k\) & \(\rho\) & \(\epsilon_{aprox}\) & \(\epsilon_{f}\) & \(\xi\) & **Cpu-Time** \\ \hline \(ACTV^{6},\alpha=1\) & 4 & 6.0917 & \(6.448\times 10^{-61}\) & 0 & \(\xi_{1}\) & 9.0684 \\ \(ACTV^{6},\alpha=-5\) & 4 & 7.0212 & \(5.485\times 10^{-75}\) & 0 & \(\xi_{1}\) & 9.1124 \\ \(ACTV^{6},\alpha=-73.25\) & 4 & 4.7204 & \(2.972\times 10^{-41}\) & \(3.558\times 10^{-239}\) & \(\xi_{1}\) & 8.6135 \\ \(ACTV^{6},\alpha=-76.89\) & 4 & 4.3741 & \(3.677\times 10^{-41}\) & \(6.341\times 10^{-236}\) & \(\xi_{1}\) & 8.8727 \\ Newton & 9 & 2.0083 & \(2.927\times 10^{-144}\) & \(4.469\times 10^{-290}\) & \(\xi_{1}\) & 2.0165 \\ \(C6_{1}\) & 4 & 6.3232 & \(1.707\times 10^{-91}\) & 0 & \(\xi_{1}\) & 2.5118 \\ \(C6_{2}\) & 4 & 6.2666 & \(4.519\times 10^{-110}\) & 0 & \(\xi_{1}\) & 2.4156 \\ \(B6,b_{1}=-3/5\) & 4 & 6.3173 & \(4.001\times 10^{-93}\) & 0 & \(\xi_{1}\) & 2.4766 \\ \(B6,b_{1}=1\) & 4 & 6.2481 & \(5.909\times 10^{-118}\) & 0 & \(\xi_{1}\) & 2.3827 \\ \(PSH6_{1},\alpha=0\) & 4 & 5.7907 & \(5.398\times 10^{-50}\) & \(2.505\times 10^{-292}\) & \(\xi_{1}\) & 8.5868 \\ \(PSH6_{1},\alpha=10\) & 4 & 7.0301 & \(1.819\times 10^{-70}\) & 0 & \(\xi_{1}\) & 8.7981 \\ \(PSH6_{2},\alpha=10\) & 4 & 4.726 & \(3.477\times 10^{-37}\) & \(7.995\times 10^{-207}\) & \(\xi_{1}\) & 8.9312 \\ \(XH6\) & 4 & 6.3144 & \(5.747\times 10^{-94}\) & 0 & \(\xi_{1}\) & 2.5340 \\ \hline \end{tabular}
\end{table}