Title: A fast algorithm for the recursive calculation of dominant singular subspaces
Authors: Mastronardi, Nicola
Van 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.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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