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Table 8 Residual errors of different iterations of QQ1 for solving \(\mathbf{F}_{7}(\mathbf{X})\)

From: On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

\(x_{i}\) \(\mathbf{e}^{(1)}\) \(\mathbf{e}^{(2)}\) \(\mathbf{e}^{(3)}\) \(\mathbf{e}^{(4)}\) \(\mathbf{e}^{(1)}\) \(\mathbf{e}^{(2)}\) \(\mathbf{e}^{(3)}\) \(\mathbf{e}^{(4)}\)
\(\Vert \mathbf{x}^{(k+1)}- \mathbf{x}^{(k)} \Vert <10^{-15}\) \(\Vert \mathbf{Fx}^{(k)} \Vert <10^{-15}\)
\(x_{1}\) 0.003 4.3e−9 4.7e−28 0.0 0.003 4.3e−9 4.2e−28 0.0
\(x_{2}\) 0.006 1.2e−9 9.3e−28 0.0 0.006 9.2e−9 9.3e−28 0.0
\(x_{3}\) 0.010 1.4e−8 1.2e−27 0.0 0.001 1.4e−8 1.2e−27 0.0
\(x_{4}\) 0.010 1.8e−8 1.5e−27 0.0 0.011 1.8e−8 1.5e−27 0.0
\(x_{5}\) 0.010 2.7e−8 2.1e−27 0.0 0.011 2.0e−8 2.1e−27 0.0
\(x_{6}\) 0.020 2.4e−8 3.0e−27 0.0 0.023 1.7e−8 3.0e−27 0.0
\(x_{7}\) 0.020 1.7e−8 3.0e−27 0.0 0.020 1.0e−8 4.1e−27 0.0
\(x_{8}\) 0.030 1.0e−8 4.1e−27 0.0 0.030 2.9e−9 4.5e−27 0.0
\(x_{9}\) 0.030 2.9e−9 4.5e−27 0.0 0.031 4.9e−9 3.6e−27 0.0
\(x_{10}\) 0.030 4.9e−9 3.6e−27 0.0 0.035 1.1e−8 1.6e−27 0.0
\(x_{11}\) 0.037 1.1e−8 1.6e−27 0.0 0.036 1.4e−8 1.4e−28 0.0
\(x_{12}\) 0.036 1.4e−8 1.4e−28 0.0 0.031 1.4e−8 1.4e−27 0.0
\(x_{13}\) 0.034 1.4e−8 1.4e−27 0.0 0.032 1.3e−8 1.4e−27 0.0
\(x_{14}\) 0.020 1.3e−8 2.1e−27 0.0 0.020 1.1e−8 1.9e−27 0.0
\(x_{15}\) 0.013 1.1e−8 2.1e−27 0.0 0.010 1.0e−8 2.1e−27 0.0
\(x_{16}\) 0.017 1.0e−8 2.4e−27 0.0 0.012 8.2e−9 2.0e−27 0.0
\(x_{17}\) 0.004 8.2e−9 1.8e−27 0.0 0.004 5.9e−8 1.3e−27 0.0
\(x_{18}\) 0.003 5.1e−9 1.5e−27 0.0 0.003 1.0e−8 1.5e−27 0.0
\(x_{19}\) 0.001 3.3e−9 6.4e−28 0.0 0.001 3.2e−9 1.6e−28 0.0