Koch, Othmar; Lubich, Christian Dynamical low-rank approximation. (English) Zbl 1145.65031 SIAM J. Matrix Anal. Appl. 29, No. 2, 434-454 (2007). Authors’ summary: For the low-rank approximation of time-dependent data matrices and of solutions to matrix differential equations, an increment-based computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rank-\(r\) matrices at the current approximation. With an appropriate decomposition of rank-\(r\) matrices and their tangent matrices, this yields nonlinear differential equations that are well suited for numerical integration. The error analysis compares the result with the pointwise best approximation in the Frobenius norm. It is shown that the approach gives locally quasi-optimal low-rank approximations. Numerical experiments illustrate the theoretical results. Reviewer: Liu Xinguo (Qingdao) Cited in 1 ReviewCited in 118 Documents MSC: 65F30 Other matrix algorithms (MSC2010) 15A23 Factorization of matrices Keywords:low-rank approximation; time-varying matrices; continuous updating; smooth decomposition; matrix differential equations; projection method; numerical experiments; error analysis PDFBibTeX XMLCite \textit{O. Koch} and \textit{C. Lubich}, SIAM J. Matrix Anal. Appl. 29, No. 2, 434--454 (2007; Zbl 1145.65031) Full Text: DOI