graeffes method

Input interpretation

Graeffe's method

Alternate name

Graeffe iteration

Definition

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by Graeffe, Dandelin, and Lobachevsky (Householder 1959, Malajovich and Zubelli 2001). Graeffe's method has a number of drawbacks, among which are that its usual formulation leads to exponents exceeding the maximum allowed by floating-point arithmetic and also that it can map well-conditioned polynomials into ill-conditioned ones. However, these limitations are avoided in an efficient implementation by Malajovich and Zubelli.
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Subject classifications

MathWorld

root-finding
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