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自动微分的基本思想与实现

Keywords: 自动微分,符号微分,差分

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Abstract:

科学计算及其应用常常需要多变量函数的有关偏导数问题的计算,通常使用的计算方法是符号微分或差分近似.对于中大规模问题来说,使用符号微分方法,成本往往非常昂贵,有时甚至不可行,在计算函数的方向梯度时,利用差分方法虽然可以降低计算成本,但得到的是近似值,而且确定恰当的差分区间也很困难.自动微分技术能以较低的成本精确计算中大规模问题函数的导数,在科学计算、工程计算及其应用领域中有着广泛的应用.

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