An Etymological Dictionary of Astronomy and Astrophysics

A method in the evaluation of polynomials which involves fewer basic operations and allows simpler computation, especially for polynomials of high degree. More specifically, the polynomial P(x) = a₀ + a₁x + a₂x² + a₃x³ + … + a_nxⁿ

can be written in the nested form as:

P(x) = a₀ + x(a₁ + x(a₂ + … + x(a_{n - 1} + a_nx) …)). For example, the polynomial P(x) = x³ - 5x² + 10x - 3 has the following nested form:
P(x) = ((x - 5)x + 10)x - 3.

Same as the → Ruffini-Horner method.

See also: → nested; → multiplication.