Cauchy交错定理对RLS算法收敛性的影响
The Impact of the Cauchy Interlace Theorem on the Convergence of the RLS Algorithm
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中文总结 AI 辅助
本文利用Cauchy交错定理分析RLS算法收敛性，提出改进初始化以加速收敛，并基于Sherman Morrison Woodbury公式给出新证明。
中文摘要 AI 辅助
本文从Cauchy交错定理的角度重新审视RLS算法的收敛性。该定理指出，Hermitian矩阵$A$及其秩一更新矩阵$\u0052hat{A} = A + u\u005cu2009u^H$的特征值是交错的。我们分析了该定理对RLS算法收敛性及其适当初始化的影响。结果表明，一种改进的初始化方法可以加速收敛时间。此外，基于Sherman Morrison Woodbury公式给出了该定理的一个新证明。
英文摘要
In this paper, we revisit the convergence of the RLS algorithm in view of the Cauchy Interlace Theorem. It states that the eigenvalues of a Hermitian matrix $A$ and of the rank one updated matrix $\hat{A} = A + u\,u^H$ interlace. We analyze the impact of this theorem on the convergence of the RLS algorithm and its suitable initialization. The results suggest an improved initialization for speeding up the convergence time. Moreover, a novel proof of the theorem is given based on the Sherman Morrison Woodbury formula.
发表机构
- University of Applied Sciences of Upper Austria（奥地利上奥地利应用科学大学）
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