The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations
T. Y. Li, TIMOTHY D. SAUER, James A. Yorke · SIAM Journal on Numerical Analysis · 1989
A procedure is introduced for solving systems of polynomial equations that need to be solved repetitively with varying coefficients. The procedure is based on the cheater’s homotopy, a continuation method that follows paths to all solutions. All solutions are found with an amount of computational work roughly proportional to the actual number of solutions. Previous general methods normally require an amount of computation roughly proportional to the total degree.