Condition number based complexity estimate for solving polynomial systems

摘要

By modifying and combining algorithms in symbolic and numerical computation, we propose a real-root-counting based method for deciding the feasibility of systems of polynomial equations. Along with this method, we also use a modified Newton operator to efficiently approximate the real solutions when the systems are feasible. The complexity of our method can be measured by a number of arithmetic operations which is singly exponential in the number of variables.