Heads up for a hot new root seeking algorithm!!

[emece67]

(01-23-2017 06:23 PM)Dieter Wrote:  

(01-23-2017 02:22 PM)emece67 Wrote:  Such Thukral algorithm is more or less useless, as it only works for zero roots. It states in the abstract that it can be used solely when the root is zero. Thus, the title f(0) = 0 is correct, the algorithm only converges to a root (yeah, with order 3 and only one function evaluation per iteration) if such root is zero.

We are talking about two different methods here. The paper on sapub.org shows a current (2016) paper by R. Thukral, quoting an older paper of the same author from 2008. Here equation [20] is the 2008 Thukral formula (with an error). This formula works for nonzero roots. Because this older Thukral formula [20] has an error Namir does not get the expected results. After a correction (cf. the original source, i.e. the 2008 Thukral paper) the formula works fine and performs similar to the other posted third-order methods, sometimes even better.

Dieter

The equation Namir used was (7) in the Thukral's 2016 paper. Such equation only converges to zero roots (as stated in the abstract and conclusions). In the same paper there's a reference to another "Thukral method" (equations (19)-(20)) which is the one in the 2008 paper by the same author. Equation (20) has an error (in the 2016 paper), but it is not related to equation (7), which is new.

Regards.