On Smale's 17th Problem: A Probabilistic Positive Solution
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Smale's 17th Problem asks “Can a zero of n complex polynomial equations in n unknowns be found approximately, on the average [for a suitable probability measure on the space of inputs], in polynomial time with a uniform algorithm?” We present a uniform probabilistic algorithm for this problem and prove that its complexity is polynomial. We thus obtain a partial positive solution to Smale's 17th Problem.
KeywordsPositive Real Number Polynomial System Coarea Formula Approximate Zero Initial Pair
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