Complex gradient and Hessian
Complex gradient and Hessian
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DOI：
10.1049/ip-vis:19941555
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发表时间：
1994-12
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影响因子：
--
通讯作者：
A. Bos
中科院分区：
文献类型：
--
作者：
A. Bos
梯度和Hessian常用于解析函数优化和数值函数优化的复值参数估计问题。在许多信号处理应用中，函数是复变量的实函数。然后，通常针对这些变量的实部和虚部进行优化；因此，有关的梯度和黑森是实的。采用这种方法的原因是为了避免在复杂变量的梯度和黑森函数的定义和解释方面遇到困难。为了解决这些困难，提出了复梯度和Hessian的定义。所提梯度与实际梯度和Hessian完全相容，并通过简单的线性变换相互关联。所提出的结果是Brandwood（1983）关于复梯度的结果的推广。
The gradient and Hessian are often used in analytical and numerical function optimisation complex valued parameter estimation problems. In a number of signal processing applications the function is a real function of complex variables. Then the optimisation is usually carried out with respect to the real and imaginary part of these variables; therefore, the gradient and Hessian concerned are real. The reason for this approach is to avoid difficulties with the definition and interpretation of the gradient and Hessian with respect to the complex variables. Definitions of a complex gradient and Hessian are proposed to solve these difficulties. The proposed and the real gradient and Hessian are fully compatible and are related by simple linear transformations. The results presented are an extension of a result by Brandwood (1983) concerning a complex gradient.