On Smale's 17th Problem: A Probabilistic Positive Solution
- 140 Downloads
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
Unable to display preview. Download preview PDF.