Solving systems of polynomial equations

Solving Systems of Polynomial Equations

Solving Systems of Positive Polynomial Equations

In this thesis, we consider equation systems of the form X1 = f1(X1, . . . ,Xn) .. Xn = fn(X1, . . . ,Xn) where fi(X1, . . . ,Xn) is, for all i ∈ {1, . . . , n}, an expression built up from real-valued variables X1, . . . ,Xn, nonnegative real constants, and the operators multiplication, addition, minimum and maximum. We call such an equation system positive and denote it in vector form by X = ...

Solving Polynomial Equations

Solving Monotone Polynomial Equations

We survey some recent results on iterative methods for approximating the least solution of a system of monotone fixed-point polynomial equations.

Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations

The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaustive search for small fields, and a Gröbner base algorithm for large fields. Gröbner base algorit...