Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we introduce a new method to deduce matrix perturbation bounds, which we call "contour bootstrapping". As applications, we work out several new bounds for eigensubspace computation and low rank approximation. Next, we use these bounds to study utility problems in the area of differential privacy.

翻译：矩阵扰动界在谱算法的设计与分析中起着至关重要的作用。本文提出了一种推导矩阵扰动界的新方法，我们称之为“轮廓自助法”。作为应用，我们推导出了若干用于特征子空间计算与低秩逼近的新界。接着，我们利用这些界来研究差分隐私领域的效用问题。