摘要In this paper, we study the efficiency issue of inexact Newton-type methods for smooth unconstrained optimization problems under standard assumptions from theoretical point of view by discussing a concrete Newton-PCG algorithm. In order to compare the algorithm with Newton's method, a ratio between the measures of their approximate efficiencies is investigated. Under mild conditions, it is shown that first, this ratio is larger than 1, which implies that the Newton-PCG algorithm is more efficient than Newton's method,and second, this ratio increases when the dimension n of the problem increases and tends to infinity at least at a rate ln n/ln 2 when n →∞, which implies that in theory the NewtonPCG algorithm is much more efficient for middle- and large-scale problems. These theoretical results are also supported by our preliminary numerical experiments.