12th International Congress on Computational and Applied Mathematics location:Leuven, Belgium date:July 10-14, 2006
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 a given sequence amounts to a singular value decomposition based compression. 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.
Algorithms proposed in the literature compute the left and right dominant subspaces of A recursively, with O(m
× k + k 3) computational complexity, where k ≪ m is an estimate of the size of such subspaces. Sometimes, k can be moderately large. In this paper an algorithm for computing the left and right dominant subspaces of A recursively requiring O(m×k + k2 ) ﬂoating points operations is proposed.