一个Newton-PCG型算法和它的效率分析

A Newton-PCG Like Algorithm and Its Theoretical Efficiency

大量的数值实验表明Newton-PCG型算法很有效,但缺乏理论上的保证.最近在文[7]中,从理论上证明了该类算法比Newton法有效.本文取消了文[7]中的过强的假设条件,在标准假设下得到了一个更有效的算法.

It is shown by a large amount of numerical experiments that the Newton-PCG like algorithms are generally very successful. But unfortunately short of theoretical justification on its efficiency. Recently, a theoretical analysis of the efficiency is developed in [7], which shows that the efficiency of the Newton-PCG like algorithm is theoretical superior to that of Newton's method. In this paper, the assumption in [7] is weakened to a more general case, and the encouraging theoretical analysis on the efficiency of the Newton-PCG like algorithm is obtained.