Residual (numerical analysis)

Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find x such that

${\displaystyle f(x)=b.}$

Given an approximation x₀ of x, the residual is

${\displaystyle b-f(x_{0})}$

that is, "what is left of the right hand side" after subtracting f(x₀)" (thus, the name "residual": what is left, the rest). On the other hand, the error is

${\displaystyle x-x_{0}}$

If the exact value of x is not known, the residual can be computed, whereas the error cannot.