Checking RSC criteria for extended Dixon resultant by interpolation method

Dixon resultant method can eliminate many variables simultaneously. It is often used to solve a system of polynomial equations. However, the Dixon matrix is often singular, and the Dixon resultant vanishes identically yielding no information about solutions for many algebraic and geometry problems. So, extended Dixon method (KSY method) was proposed for the case when the Dixon matrix is singular, but satisfies RSC criteria. However, checking RSC criteria and extracting a maximum nonsingular submatrix of Dixon matrix are symbolic methods, which restrict extended Dixon method to be applied in more fields. In this paper, based on polynomial interpolation theory, an efficient numerical algorithm is developed to check RSC criteria and to extract a maximum nonsingular submatrix of singular Dixon matrix. Combining with interpolation methods for computing determinant, our method can solve larger scale problems. Furthermore, our method can be carried out parallel.