线性映射的移动平均迭代
Moving-Average Iteration of Linear Maps
AI总结：
本文研究固定复矩阵的移动平均迭代，在Krasnoselskii和Mann迭代框架下给出渐近稳定性的谱条件，推导稳定区域的显式公式，并证明其开、凸、半代数性及随窗口长度严格递增，确定极限区域。
AI中文摘要：
我们考虑固定复矩阵的移动平均迭代，并将该理论置于Krasnoselskii和Mann迭代的一般背景下。针对固定窗口宽度，给出了移动平均迭代渐近稳定性的必要且充分的谱条件。对于复平面中相应的稳定区域，推导出了显式公式，并证明了该区域是开的、凸的且半代数的。这些区域被证明随窗口长度严格递增，且当窗口大小趋于无穷时，确定了极限稳定区域。
英文摘要：
We consider moving-average iteration for fixed complex matrices and place the theory in the general context of Krasnoselskii and Mann iteration. Necessary and sufficient spectral conditions for the asymptotic stability of moving-average iteration are presented in dependence on the fixed window width. For the corresponding region of stability in the complex plane explicit formulas are derived and it is shown that the region is open, convex and semi-algebraic. The regions are shown to be strictly increasing in the window length and the limiting stability region is determined as the window size tends to infinity.
