A general framework for SVD flows and joint SVD flows

The paper presents a general framework for the development of continuous algorithms for SVD and joint SVD problems. The framework for SVD is derived based on gradient flows on unitary groups. Two previous examples of SVD flows discovered heuristically are derived systematically using the framework. The framework for SVD is extended for joint SVD problems, and a new continuous algorithm for joint SVD is derived using the framework. The work described gives a clear perspective on SVD and joint SVD flows as well as a means for the development of new continuous algorithms.