Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

Accuracy Comparison of Implant Impression Techniques: A Systematic Review

Background: Several studies link the seamless fit of implant-supported prosthesis with the accuracy of the dental impression technique obtained during acquisition. In addition, factors such as implant angulation and coping shape contribute to implant misfit. Purpose: The aim of this study was to identify the most accurate impression technique and factors affecting the impression accuracy. Material and Methods: A systematic review of peer-reviewed literature was conducted analyzing articles published between 2009 and 2013. The following search terms were used: implant impression, impression accuracy, and implant misfit.A total of 417 articles were identified; 32 were selected for review. Results: All 32 selected studies refer to in vitro studies. Fourteen articles compare open and closed impression technique, 8 advocate the open technique, and 6 report similar results. Other 14 articles evaluate splinted and non-splinted techniques; all advocating the splinted technique. Polyether material usage was reported in nine; six studies tested vinyl polysiloxane and one study used irreversible hydrocolloid. Eight studies evaluated different copings designs. Intraoral optical devices were compared in four studies. Conclusions: The most accurate results were achieved with two configurations: (1) the optical intraoral system with powder and (2) the open technique with splinted squared transfer copings, using polyether as impression material.