`horner`

Horner (nested) form of a polynomial.

Category: Mathematics > Formula Manipulation and Simplification

Syntax

R = horner(P)

Rewrites the polynomial P in nested multiplication form.

Description

Writing x^3 + 2*x^2 + 3*x + 4 as x*(x*(x + 2) + 3) + 4 evaluates the polynomial with only additions and multiplications and no powers. This takes fewer operations and is numerically better behaved, which is why it is the usual way to evaluate polynomials by machine.

Input arguments

P: Symbolic polynomial.

Output arguments

R: Equivalent expression with the nesting x*(x*(a*x + b) + c) + d.

Example

Nested form of a cubic

syms x
horner(x^3 + 2*x^2 + 3*x + 4)

Output

ans = x*(x*(x + 2) + 3) + 4

See also

polyval expand collect poly2sym matlabFunction