Gradient methods of maximization.

is an approximation to the point c. Assuming that x ( 0 ) is sufficiently close to c, we may obtain an improved approximation to c by considering the first few terms of the Taylor expansion of fix) about # ( 0 ) . Presumably, the greater the number of terms of the expansion that we consider, the better will be our improved approximation and the more rapidly will the corresponding iterative procedure converge. On the other hand, increasing the number of terms of the expansion involves the calculation of higher order derivatives and increases considerably the computational cost of each iteration.