Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find x such that =. Given an approximation x 0 of x, the residual is − whereas the error is − If the exact value of x is not known, the residual can be computed, whereas the error cannot. Residual of the approximation of a function Similar terminology is used dealing with differential, integral and functional equations. For the approximation of the solution of the equation