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Solving Quadratic Recurrence By Matrix Exponentiation
By code_hard123, history, 9 years ago, In English

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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9 years ago, # |
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No, only linear recurrences terms can be calculated using matrix exponentiation.

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    9 years ago, # ^ |
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    Cant it be solved any other ways?

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      9 years ago, # ^ |
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      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.

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9 years ago, # |
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These type of equation are known as Quadratic Map. Maybe this can help you.

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