Note on Jacobi’s method for approximating dominant roots

In 1834 Jacobi gave a method for approximating dominant roots of a polynomial. In 2002 Mignotte and Stefanescu showed that Jacobi’s method works only when the dominant roots are simple. In this note, we show that Jacobi’s method can still be useful even when the dominant roots are not simple, if we use it for approximating the “distinct” dominant roots.