A Deterministic Algorithm to Compute Approximate Roots of Polynomial Systems in Polynomial Average Time
- First Online:
- Cite this article as:
- Lairez, P. Found Comput Math (2016). doi:10.1007/s10208-016-9319-7
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum–Shub–Smale model with square root. It rests upon a derandomization of an algorithm of Beltrán and Pardo and gives a deterministic affirmative answer to Smale’s 17th problem. The main idea is to make use of the randomness contained in the input itself.