Lizhi, "A new fourth-order iterative- method for finding multiple roots
of nonlinear equations," Applied Mathematics and Computation, vol.
Inspired by the work in this direction, here we present a third order scheme of one-point methods without memory for multiple roots
. The proposed scheme involves one evaluation of f, f', and f" each per step.
Let [gamma] be a given polar, not a multiple root
of f(z, w) (fixed in what follows), i.e., f([gamma](w), w) [not equal to] 0.
The Generalized Extrapolated Newton-Raphson Method (GEN-R) considered by Vatti VBK et, al  for the multiple root
of equation (1.1) is given as
It is to note that the method (1.4) is generally applied for finding a multiple root
of equation (1.1) knowing the multiplicity of root in advance.
Values are 75% lower at the 0.5-mm distance relative to a single root system; however, water content gradients are higher for the multiple root
system than a single root at the 1.5-mm distance for 2 and 4 h.
g., CAS(1)) may mean that a multiple root
is presented in one time.
In this case [a.sub.1] is a multiple root
and for the example given is a root of multiplicity three.
PCI Express was not designed to support this environment and so non-transparent bridges are introduced to support a multiple root
Hurricane winds and seas batter them--here their multiple root
system is a great advantage.
I face a room of 30 seniors who look as though they're about ready to have multiple root
canals instead of spending one class period in senior English.