Recursive Formulas

(Math | Advanced | Recursive Formulas | (A))

Recursive Formulas for (A)

Explicit form:

Find (A), where A is a real number > 0.

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)
x_n+1 = (x_n/2)(3 - ax_n²)

Reiterate about 5 or 6 times then do y with that result.

y_i+1 = y_i + (x_n/2)(a - y_i²)

Reiterate until required precision attained.

A = y_i * 2^exp

 
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