Graeffe's method

Graeffe's method, also called the Dandelin-Lobachesky-Graeffe method, is an algorithm for finding all of the roots of a polynomial. It was developed independently by Germinal Pierre Dandelin in 1826 and by Lobachevsky in 1834, and in 1837 Karl Heinrich Graeffe also discovered the principal idea of the method. The method separates the roots of a polynomial by squaring them repeatedly. This squaring of the roots is done implicitly, that is, by working only on the coefficients of the polynomial. Finally, Vieta's formulas are used in order to approximate the roots.