Horner's rule for polynomial evaluation
Horner's rule for polynomial evaluation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A fast scheme for evaluating a polynomial such as:
when
.
Is to arrange the computation as follows:
And compute the result from the innermost brackets outwards as:
coefficients = [-19, 7, 4, 6] # list coefficients of all x^0..x^n in order x = 3 reversedcoeffs = reverse(coefficients) accumulator = reversedcoeffs[0] for (i=1; i<length(reversedcoffs); i++){ accumulator = ( accumulator * x ) + reversedcoeffs[i] } # accumulator now has the answer
Task Description
- Create a routine that takes a list of coefficients of a polynomial in order of increasing powers of x; together with a value of x to compute its value at, and return the value of the polynomial at that value using Horner's rule.
C.f: Formal power series
Python
<lang python>>>> def horner(coeffs, x): acc = coeffs[-1] for c in reversed(coeffs[:-1]): acc = acc * x + c return acc
>>> horner( (-19, 7, 4, 6), 3) 200</lang>