On the complexity of calculation of differentials and gradients
On the complexity of calculation of differentials and gradients
复制标题
关于微分和梯度计算的复杂性
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
I. Gashkov
中科院分区：
文献类型：
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作者：
S. Gashkov;I. Gashkov
我们获得了根据该功能的电路复杂性，从一个任意基本函数的一个到k的差异系统系统的复杂性实现的界限。对于Jacobian和Hessian矩阵的实现的复杂性，获得了相似的界限。我们指出了一些应用程序，以减少多个变量，线性转换和二次形式的多项式复杂性的界限。
We obtain bounds for the complexity of circuit realisation of the system of differentials of orders from one to k of an arbitrary elementary function in terms of the circuit complexity of this function. Similar bounds are obtained for the complexities of realisation of the Jacobian and Hessian matrices. We point out some applications to deduction of bounds for complexities of polynomials in several variables, linear transformations, and quadratic forms.