论文标题
在Hyper-Lyapunov夹杂物上
On the hyper-lyapunov inclusions
论文作者
论文摘要
Gantmacher-Lyapunov定理（1950年代）的特征是矩阵的光谱位于复杂平面的右侧。在这里，该结果将精制成超裂解曲线的矩阵，其频谱位于右半平面内的某些磁盘中。 这些磁盘在反转下变为关闭，当它们的半径接近无穷大时，最初的结果就会恢复。 超裂解的夹杂物是通过二次基质不等式提出的，因此，类似的高stein矩阵矩阵集中的光谱位于亚单位磁盘内。 作为副产品，表明这些磁盘在反转下关闭，是理解矩阵计算中使用的矩阵符号函数迭代方案的自然工具。
Gantmacher-Lyapunov Theorem (1950's) characterizes matrices whose spectrum lies in the right-half of the complex plane. Here this result is refined to Hyper-Lyapunov inclusion for matrices whose spectrum lies in some disks within the right-half plane. These disks turn to be closed under inversion, and when their radius approaches infinity, the original result is recovered. Hyper-Lyapunov inclusions are formulated through Quadratic Matrix Inequalities and so are the analogous Hyper-Stein sets of matrices whose spectrum lies within a sub-unit disk. As a by-product, it is shown that these disks closed under inversion, are a natural tool to understanding the Matrix Sign Function iteration scheme, used in matrix computations.
