Iterative Methods For Reciprocal Square Roots
The following are iterative methods for finding the reciprocal square root of S which is . Once it has been found, find by simple multiplication: . These iterations involve only multiplication, and not division. They are therefore faster than the Babylonian method. However, they are not stable. If the initial value is not close to the reciprocal square root, the iterations will diverge away from it rather than converge to it. It can therefore be advantageous to perform an iteration of the Babylonian method on a rough estimate before starting to apply these methods.
- One method is found by applying Newton's method to the equation . It converges quadratically:
- Another iteration obtained by Halley's method, which is the Householder's method of order two, converges cubically, but involves more operations per iteration:
Read more about this topic: Methods Of Computing Square Roots
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