Title: A fast algorithm for the recursive calculation of dominant singular subspaces Authors: Mastronardi, NicolaVan Barel, Marc ×Vandebril, Raf # Issue Date: Sep-2008 Publisher: Elsevier Series Title: Journal of Computational and Applied Mathematics vol:218 issue:2 pages:238-246 Abstract: In many engineering applications it is required to compute the dominant subspace of a matrix A of dimension $m \times n$, with m > n. Often the matrix A is produced incre- mentally, so all the columns are not available simultaneously. This problem arises, e.g., in image processing, where each column of the matrix A represents an image of a given sequence leading to a singular value decomposition based compression [1]. Furthermore, the so called proper orthogonal decomposition approximation uses the left dominant subspace of a matrix A where a column consists of a time instance of the solution of an evolution equation, e.g., the flow field from a fluid dynamics simulation. Since these flow fields tend to be very large, only a small number can be stored efficiently during the simulation, and therefore an incremental approach is useful [7].In this paper an algorithm for computing an approximation of the left dominant subspace of size k of $A\in R^{m\times n}$, with $k < m,n$, is proposed requiring at each iteration $O(mk + k^2)$ floating point operations. Moreover, the proposed algorithm exhibits a lot of parallelism that can be exploited for a suitable implementation on a parallel computer. URI: http://dx.doi.org/10.1016/j.cam.2006.12.032 ISSN: 0377-0427 Publication status: published KU Leuven publication type: IT Appears in Collections: Numerical Analysis and Applied Mathematics Section