A Comprehensive Comparison of Various Algorithms for Efficiently Updating Singular Value Decomposition Based Reduced Order Models

Abstract

Efficiently updating an SVD-based data representation while keeping accurate track of the data mean when new observations are coming in is a common objective in many practical application scenarios. In this paper, two different SVD update algorithms capable of treating an arbitrary number of new observations are introduced following the symmetric EVD philosophy. These methods are compared to an SVD update method known from the literature. The comparison criterion of interest is the theoretical computational complexity, it being understood that the dimension of the observation vectors is much larger than the number of observations. From this point of view, a hierarchy of methods is derived, and the computational savings of the update strategies pursuing the symmetric EVD approach are demonstrated. It is exposed, how the compression level of the initial SVD model affects the performance of these algorithms and the break point where one method becomes more efficent than the other is determined. In addition, simple rules of thumb are derived for easing the choice of an algorithm valid in most practical scenarios.