Numerical certification
Numerical certification is the process of proving that a numerical computation produced a correct result. In numerical computational mathematics, specifically numerical algebraic geometry, approximations to solutions of systems of equations are computed. The coordinates of these solutions are not exact. Hence, doubt is cast on the correctness of the solutions. Certification is a method of proving the correctness of a solution.
The foundation of numerical certification is Smale's alpha theory, a body of mathematical theory and techniques for proving that a solution is in the domain of quadratic convergence for Newton's method.[1]
Category:Algebraic geometry
Category:Nonlinear algebra
- ^ Hauenstein, Jonathan; Sottile, Frank (2012). "Algorithm 921: alphaCertified: certifying solutions to polynomial systems". ACM Transactions on Mathematical Software (TOMS). 38 (4): 28. doi:10.1145/2331130.2331136.