\input zb-basic
\input zb-ioport
\iteman{io-port 06063167}
\itemau{Zhang, Li; Jian, Shuyuan}
\itemti{Comments on: ``A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations''.}
\itemso{J. Comput. Appl. Math. 236, No. 17, 4344-4347 (2012).}
\itemab
Summary: In this note a simple counter example shows that the proof of Lemma 3.3 in [1, W. Cheng, Y. Xiao and Q. Hu, A family of derivative-free conjugate gradient methods for large-scale nonlinear systems of equations, J. Comput. Appl. Math. 224 (2009) 11-19] is not correct, which implies that Lemma 3.2 in [1] is not enough to ensure Lemma 3.3 in [1]. A new proof is given, which leads to a stronger result than Lemma 3.2 in [1]. And this result not only guarantees that Lemma 3.3 in [1] holds, but also improves the corresponding global convergence Theorem 3.1 in [1].
\itemrv{~}
\itemcc{}
\itemut{nonlinear equations; conjugate gradient method; global convergence}
\itemli{doi:10.1016/j.cam.2012.03.029}
\end