Re: Lyuka and the Ostrowski method's for Root Seeking Message #2 Posted by Lyuka on 20 Aug 2011, 11:03 a.m., in response to message #1 by Namir
Hi,
The Ostrowski's method is a kind of root finding algorithm that uses reverseinterpolation to approximate the root.
So, any other interpolation, such as Lagrange interpolation, can be used as a root finding algorithm.
If you use that of n=3, a recurrence equation
can be used instead of Ostrowski's
This can be tested replacing a line in _ost.c
Quote:
t = (h * a  b) / (h  1.0);
by
Quote:
t = a * e * f * (f  e)  b * d * f * (f  d) + c * d * e * (e  d);
t /= (f  e) * (f  d) * (e  d);
Though the convergence of the method shown above is almost quadratic (order of about 1.8) for a zero of multiplicity 1 in a neighborhood of the zero, it's NOT recommended as it tends to diverge when the guess is not near the zero.
IMHO, the most important thing as a root finding algorithm is not
the order of convergence, but the stability of convergence, i.e. ability to find a root with very few chance of divergence.
Regards,
Lyuka
