Little math problem(s) January 2019

[Paul Dale]

As the function approaches zero, the relative error will become controllable.

Given the function F(x), make an estimate ϕ. Due to the relative error, ϕ lies between 0.8 F(x) and 1.2 F(x). i.e. |F(x) - ϕ| ⩽ 0.2 F(x). Now, take the function G(x) = F(x) - ϕ. Make an estimate of this function ζ. Again, |G(x) - ζ| ⩽ 0.2 G(x). This means |F(x) - (ϕ - ζ)| ⩽ 0.04 F(x). Repeat.

Pauli