  Many physical systems can be described in terms of matrix models that we
often cannot solve analytically. Fortunately, they can be studied numerically
in a straightforward way. Many commonly used algorithms follow the Monte Carlo
method, which is efficient for small matrix sizes but cannot guarantee
ergodicity when working with large ones. In this paper, we propose an
improvement of the algorithm that, for a large class of matrix models, allows
to tunnel between various vacua in a proficient way, where sign change of
eigenvalues is proposed externally. We test the method on two models: the pure
potential matrix model and the scalar field theory on the fuzzy sphere.
