Smoothness of Schatten norms and sliding-window matrix streams

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+ϵ)-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.