  In latest years, several advancements have been made in symbolic-numerical
eigenvalue techniques for solving polynomial systems. In this article, we add
to this list. We design an algorithm which solves systems with isolated
solutions reliably and efficiently. In overdetermined cases, it reduces the
task to an eigenvalue problem in a simpler and considerably faster way than in
previous methods, and it can outperform the homotopy continuation approach. We
provide many examples and an implementation in the proof-of-concept Julia
package EigenvalueSolver.jl.
