To obtain an approximated value of

**sqrt(a)**, one can use Newton's method:

with a given real

**x[0]**. This can be easily implemented in computer programs such as MATLAB or SCILAB, but today I will represent this as a feedback system.

First, the iteration can be represented by

where

**denotes the shift operator***σ*
In control theory or signal processing, this operator is also denoted by

**z**. Next, the iteration is divided into two parts,^{-1}**and***φ**, that is,***σ**
Finally, this can be represented by the following block diagram:

This is a "feedback system" for

**sqrt(2)**. You can change the initial value**x[0]**by double-clicking "**1/z**" block. Also, if you want another square root, double-click the "**Expression**" block and change "2" in the numerator to another*positive*number. But, if you feel like wilding out, use a*negative*number instead. In this case, the sequence will not converge, but show some chaotic behavior. The following is the result for "**-2**."**Related entries:**

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