The authors examine several algorithms for isolating real zeros of polynomials. These algorithms are classified as algebraic, rather than numerical. They compute exactly a sequence of disjoint intervals with rational endpoints, each of which contains exactly one real zero.

One algorithm described is due to Kronecker [1]; it is very simple, but is exponential in n, the degree of the polynomial. Another algorithm is based on Sturm sequences; its use is limited because of growth of the coefficients in the Sturm sequence. An algorithm based on Rolle’s theorem [2] produces a sequence of polynomials with smaller coefficients. A new, modified Uspensky algorithm is introduced. A correctness proof is included, and the algorithm is shown to be faster than the others.