Heads up for a hot new root seeking algorithm!!

01192017, 08:13 PM
(This post was last modified: 01192017 08:42 PM by JurgenRo.)
Post: #16




RE: Heads up for a hot new root seeking algorithm!!
(01192017 03:23 AM)Claudio L. Wrote:(01182017 11:53 PM)Namir Wrote: I am not sure that Ostrowski's method has an order 4 of convergence. Any reference that confirm this? You have to distinguish between local and global error. Plain Newton is simply Tayler series Expansion of 1st order: f(x_(n+1)) = f(x_n) + hf'(x_n) + (1/2)h^2f''(ceta), where h= x_(n+1)x_n, ceta in (x_n+1,x_n) and R:=(1/2)h^2f''(ceta) is the term defining the local error (of each step). That is, locally plain Newton is o(h^2), i.e. quadratic. The global error though (the accumulated error of all N steps ) is o(Nh^2)=o(h), i.e. linear behavior. Normally you are interested in the total accumulated error, i.e. in the global error. So to my understanding plain Newton is a linear scheme. Juergen 

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