Laguerre's method

Laguerre's method is a root-finding algorithm tailored to polynomials, used to solve p(x) = 0 numerically for a given polynomial p(x). It is named in honour of the French mathematician Edmond Laguerre. One of its most valued properties is practical reliability: from extensive empirical study it is very close to being a sure-fire method, almost guaranteed to converge to some root of the polynomial no matter which initial guess is chosen. For computer computation, however, more efficient methods are known that are guaranteed to find all roots, or all real roots, so Laguerre's method is best understood as a robust classical technique rather than the most efficient modern one.