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## The convergence rate

We can now analyze which of the particular choices of is more appropriate as far as the convergence rate is concerned.

If we consider the general form of the square root iteration

we can estimate the convergence rate by the difference between the actual estimation at step (n+1) and the analytical value . For the general case, we obtain

or
 (7)

 sqroot Figure 2 Convergence plots for different recursive algorithms, shown in Table 1.

The possible selections for from Table 1 clearly show that the recursions described in the preceding subsection generally have a linear convergence rate (that is, the error at step n+1 is proportional to the error at step n), but can converge quadratically for an appropriate selection of the parameter , as shown in Table 7. Furthermore, the convergence is faster when is closer to .