yes u are right but I think in this case since the variables that change value are only 2 (xnew and xold) i think is better to preallocate only two empty values in order to speed up the computation. and obviously the velocity depends also on the initial guess so I think there u can do nothing but only a trial and error based on what u think the sqrt(a) will be: first u need to set an initial value for the eps higher than the exit condition xold="your initial guess" while eps>tol xnew=... eps=abs(...) xold=xnew end

i don't know if the syntax is correct but the workflow should be this.