1 Erratum to: J Math Chem (2015) 53:430–449 DOI 10.1007/s10910-014-0432-z

The following errors were inadvertently overlooked in the original publication, and it has been corrected with this erratum.

Page 8. The first line of the formula (13) says: “\(y^{(k+1)}=x^{(k)}-\alpha [F^{\prime }(x^{(k)})]^{-1}F(x^{(k)})\)”, replace by \(y^{(k)}=x^{(k)}-\alpha [F^{\prime }(x^{(k)})]^{-1}F(x^{(k)})\), and the last two lines of same formula are repetitions: delete.

Page 9. Line 13 says: “where \(e_k=x^{(k)}-\xi \) and \(C_q=\left( \frac{1}{q!}\right) [f^{\prime }(\xi )]^{-1}F^{(q)}(\xi ), q \ge 2\).” Replace by \(e_k=x^{(k)}-\xi \) and \(C_q=\left( \frac{1}{q!}\right) [F^{\prime }(\xi )]^{-1}F^{(q)}(\xi ), q \ge 2\).

Page 10. The line 20 says: “\(e_{k+1} = H_2^{\prime }e_k^{2}+H_3^{\prime }e_k^{2}+H_4^{\prime }e_k^{2} +{\mathcal {O}}[e_{k}^5]\)”. Replace by \(e_{k+1} = H_2^{\prime }e_k^{2}+H_3^{\prime }e_k^{3}+H_4^{\prime }e_k^{4} +{\mathcal {O}}[e_{k}^5]\).

Page 10. The line 21 says: “where \(H_1^{\prime } = \frac{1}{a_1}(1+a_1(b_{1}-1))C_2\). Replace by: where \(H_2^{\prime } = \frac{1}{a_1}(1+a_1(b_{1}-1))C_2\).

Page 11. The line 6 says: “\(G(x^{(k)}, y^{(k)})=\frac{1}{a_1}[(1+a_{1}b_2-2a_1)I-a_1(b_{2} -2) [F^{\prime }(x^{(k)})]^{-1}[x^{(k)}, y^{(k)}; F]]^{-1}\)”. Replace by: \(G(x^{(k)}, y^{(k)})=\frac{1}{a_1}[(1+a_{1}b_2-2a_{1})I-a_1^2(b_{2} -2)[F^{\prime }(x^{(k)})]^{-1}[x^{(k)}, y^{(k)}; F]]^{-1}\).

Page 11. The line 19 says: “\(x^{(k+1)}=y^{(k)}-(I-2[F^{\prime }(x^{(k)})]^{-1}[x^{(k)}, y^{(k)}; F]) [F^{\prime }(x^{(k)})]^{-1}F(y^{(k)})\)”. Replace by \(x^{(k+1)}=y^{(k)}-(3I-2[F^{\prime }(x^{(k)})]^{-1}[x^{(k)}, y^{(k)}; F]) [F^{\prime }(x^{(k)})]^{-1}F(y^{(k)})\).

Page 11. The line 25 says: “\(x(k+1)=y^{(k)}-\frac{1}{a_1}[(1-a_{1})I+a_1[F^{\prime }(x^{(k)})]^{-1} [x^{(k)}, y^{(k)}; F]]^{-1}\)”. Replace by \(x^{(k+1)}\!=\!y^{(k)}-\frac{1}{a_1}[(1-a_{1})I+a_1^2[F^{\prime }(x^{(k)})]^{-1} [x^{(k)}\!, y^{(k)}; F]]^{-1}\)

Page 11. The line 26 says: “\(F(x^{(k)})+\frac{1}{a_1}[(2a_{1}-1)I-[F^{\prime }(x^{(k)})]^{-1}[x^{(k)}, y^{(k)}; F]] [F^{\prime }(x^{(k)})]^{-1}F(y^{(k)})\)”. Replace by \(F(x^{(k)})+\frac{1}{a_1}[(2a_{1}-1)I-[F^{\prime }(x^{(k)})]^{-1} [x^{(k)}, y^{(k)}; F]] [F^{\prime }(x^{(k)})]^{-1}F(y^{(k)})\).

Page 15. The line 1 says: “Table 3 Test functions and results for nonlinear systems, \(F_1\) and \(F_2\)”. Replace by: Table 3 Test functions and results for nonlinear functions, \(F_1\) and \(F_2\).

Page 15. The line 3 says: “\(F_1(x_1, x_2)=(\exp x_1 \exp x_2+x_1\cos x_2, x_1+x_2-1 \,x^{(0)}=(3, -2)\) and \(\xi _1 \approx \)”. Replace by \(F_1(x_1, x_2)=(\exp x_1 \exp x_2+x_1\cos x_2, x_1+x_2 -1) \,x^{(0)}=(3, -2)\) and \(\xi _1 \approx \).

Page 15. The line 4 says: “\(3.4675009642402, \xi _2 \approx -2.4675009642402\)”. Replace by: \(3.4706309600316, \xi _2 \approx -2.4706309600316\).

Page 16. The line 1 says: “Table 4 Test functions and results for nonlinear systems, \(F_3\) and \(F_4\)”. Replace by: Table 3 Test functions and results for nonlinear functions, \(F_3\) and \(F_4\).

Page 16. The line 4 says: “\(-0.8452567390376772; \xi _2 \approx -0.7481414932526368\)”. Replace by: \(-0.8452567390376772, \xi _2 \approx 0.7481414932526368\).