A new algorithm for computing certified numerical approximations of the roots of a zero-dimensional system

摘要

This paper provides a new method for computing numerical approximations of the roots of a zero-dimensional system. It works on general systems, even those with multiple roots, and avoids any arbitrary choice of linear combination of the multiplication operators. It works by computing eigenvectors (or a basis of the full invariant subspaces). The sparsity/structure of the multiplication operators by one variable can also be taken into account.