Large matrices are often accessed as a row-order stream. We consider the setting where rows are time-sensitive (i.e. they expire), which can be described by the sliding-window row-order model, and provide the first $(1+\epsilon)$-approximation of Schatten $p$-norms in this setting. Our main technical contribution is a proof that Schatten $p$-norms in row-order streams are smooth, and thus fit the smooth-histograms technique of Braverman and Ostrovsky (FOCS 2007) for sliding-window streams.

翻译：大型矩阵通常作为行序流访问。 我们考虑行的时间敏感度(即行龄到期)的设置,这种设置可以通过滑动窗口行序模型来描述,并在这一设置中提供第一个(1 ⁇ -epsilon)美元(美元-诺尔姆)的Schatten $p$-诺尔姆(美元-诺尔姆),我们的主要技术贡献证明行序流中Schatten $p$-诺姆(美元-诺姆)是顺畅的,因此符合Braverman和Ostrovsky(FOCS 2007年)滑动窗口流的平滑历史图技术。