【摘要】 一类新的使用符号微分的Newton-PCG型算法在文献[1]和[2]被导出来了.本文建立和研究应用自动微分的相应的Newton-PCG算法,理论分析和数值实验结果显示应用自动微分之后,目标函数的维数或复杂性越大,Newton-PCG算法对Newton法的改进越显著.更多还原

【Abstract】 A new Newton-PCG like algorithm with the usual symbolic differentiation (SD) is derived in [1] and [2]. In this paper, we consider the corresponding Newton-PCG algorithm with automatic differentiation (AD). The results by theoretical analysis and preliminary numerical experiments indicate that the larger the dimension or the cost of the objective function evaluation is, the more the improvement of the Newton-PCG algorithm over Newton method will be.更多还原