Horner's method

In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S.) is either of two things:

The latter is also known as Ruffini–Horner's method.

These methods are named after the British mathematician William George Horner, although they were known before him by Paolo Ruffini and, six hundred years earlier, by the Chinese mathematician Qin Jiushao.

Given the polynomial

where ${\displaystyle a_{0},\ldots ,a_{n}}$ are real numbers, we wish to evaluate the polynomial at a specific value of ${\displaystyle x}$, say ${\displaystyle x_{0}}$.

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