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Recursive Formulas
(Math | Advanced | Recursive Formulas | [sqrt](A))

Recursive Formulas for [sqrt](A)

Explicit form:

Find [sqrt](A), where A is a real number > 0.
Recursive form:
Convert A to scientific notation base 2 (C++ has function "frexp" for this). Note: mantissa is ³ .5 and < 1.

Let

a = mantissa of A
exp = exponent of a
a = a * 2(exp mod 2)
exp = exp \ 2       (Note:  integer divide)
xn+1 = (xn/2)(3 - axn2)
Reiterate about 5 or 6 times then do y with that result.
yi+1 = yi + (xn/2)(a - yi2)
Reiterate until required precision attained.

[sqrt]A = yi * 2exp

Source: Jeff Yates.


  
 
  

 
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