Bernoulli's method

In numerical analysis, Bernoulli's method, named after Daniel Bernoulli, is a root-finding algorithm which calculates the root of largest absolute value of a univariate polynomial. The method works under the condition that there is only one root (possibly multiple) of maximal absolute value. The method computes the root of maximal absolute value as the limit of the quotients of two successive terms of a sequence defined by a linear recurrence whose coefficients are those of the polynomial.

Since the method converges with a linear order only, it is less efficient than other methods, such as Newton's method. However, it can be useful for finding an initial guess ensuring that these other methods converge to the root of maximal absolute value. Bernoulli's method holds historical significance as an early approach to numerical root-finding and provides an elegant connection between recurrence relations and polynomial roots.