In this short note we give certain comments and improvements of some three-step iterative methods recently considered by N.A. Mir and T. Zaman (Appl. Math. Comput. (2007) doi: 10.1016/j.amc.2007.03.071).

J. Tokumine1*, A. T. Lefor4, A. Yonei5, A. Kagaya2, K. Iwasaki2 and Y. Fukuda3 1 Department of Anesthesia, 2 Department of Surgery, and 3 Department of Internal Medicine, Seikei-kai Chiba Medical Center, 1-11-12, Minami-cho, Chuo-ku, Chiba-shi 260-0842, Japan 4 Medical Simulation Center, Jichi Medical University Hospital, 3311-1 Yakushiji, Shimotsuke-shi, Tochigi-ken 329-0498, Japan 5 Departmen...

In this paper, a published algorithm is investigated that proposes a three-step iterative method for solving nonlinear equations. This method is considered to be efficient with third order of convergence and an improvement to previous methods. This paper proves that the order of convergence of the previous scheme is two, and the efficiency index is less than the corresponding Newton’s method. I...

BACKGROUND The long-axis view and in-plane needle approach (LAX-IP) for ultrasound-guided central vein catheterization is considered ideal because of the quality of real-time imaging. We describe a novel technique, using a step-by-step procedure, to overcome the pitfalls associated with the LAX-IP. This study was undertaken to demonstrate the clinical utility of this approach. METHODS All ope...