Halley's iterative formula based on Padé approximation and its modifications

Padé approximation is one of very important rational approximations. By means of Padé approximation, Halley's iterative formula is reconstructed. Considering that derivatives can be approximated by divided differences, some variants of Halley's iterative schemes which avoid computing derivatives are obtained. At last numerical examples are presented to show that these iterative schemes are effective. Copyright © 2012 Binary Information Press.