Title: A fast algorithm for the recursive calculation of dominant singular subspaces
Authors: Mastronardi, Nicola
Van Barel, Marc
Vandebril, Raf
Issue Date: Sep-2006
Publisher: K.U.Leuven, Department of Computer Science
Series Title: TW Reports vol:TW468
Abstract: In many engineering applications it is required to compute the dominant subspace of a matrix A of dimension m
× n, with m ≫ n. Often the matrix A is produced incrementally, 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 agiven 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
∈ Rm×n, with k≪ m, n, is proposed requiring at each iteration O(mk + k2 ) floating point operations. Moreover, the proposed algorithm exhibits a lot of parallelism that can be exploited for a suitable implementation on a parallel computer.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Electrical Engineering - miscellaneous
NUMA, Numerical Analysis and Applied Mathematics Section

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