Skip to main content

Theory and Modern Applications

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