Polynomial computation numerical errors

[zorro]

Hi friends,

Suppose I have to evaluate a polynomial than can be expressed in long form as

p(x) = a_n*xⁿ + a_n-1*x^n-1 + ... + a₁*x + a₀

If I'm not wrong, the nested Horner form:

p(x) = (...((b_n*x + b_n-1)*x + ...)*x + ...)*x + b₀

is numerically better (usually has less numerical error than the first form).
Can somebody give a reference that justify this? In what conditions it is true?

Best regards

Z