论文标题
符号特征值的一阶灵敏度分析
First order sensitivity analysis of symplectic eigenvalues
论文作者
论文摘要
每$ 2n \ times 2n $正面确定的矩阵$ a $都有$ n $阳性数字$ d_1（a）\ leq \ ldots \ ldots \ leq d_n（a）$ a $ a $ a $ a $ a symplectic eigenvalues $ A $A。在本文中，我们表明存在$ d_m $的定向衍生物并得出其表达式。我们还讨论了$ d_m $的各种细分属性，例如Clarke和Michel-Penot细分。
For every $2n \times 2n$ positive definite matrix $A$ there are $n$ positive numbers $d_1(A) \leq \ldots \leq d_n(A)$ associated with $A$ called the symplectic eigenvalues of $A.$ It is known that $d_m$ are continuous functions of $A$ but are not differentiable in general. In this paper, we show that the directional derivative of $d_m$ exists and derive its expression. We also discuss various subdifferential properties of $d_m$ such as Clarke and Michel-Penot subdifferentials.
