Hi all ,
Is it possible to calculate the Nth (1 <= N <= 1e18) term of following quadratic recurrence using matrix exponentiation.
F(i) = a * F(i -1) * F(i -1) + b * F(i -1) + c , where a , b , c are non negative constants and F0 (Initial Term) is given.
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No, only linear recurrences terms can be calculated using matrix exponentiation.
Cant it be solved any other ways?
If the modulus is small, then find a period. For some a, b, c there might be interesting formulae, but none faster than O(n) that I'm aware of.
thanks for sharing your idea. :)
These type of equation are known as Quadratic Map. Maybe this can help you.
thanks. It helped :)