Journal of Computational and Applied Mathematics
Parallel tri- and bi-diagonalization of bordered bidiagonal matrices
Parallel Computing
An eigenspace update algorithm for image analysis
Graphical Models and Image Processing
Recursive Calculation of Dominant Singular Subspaces
SIAM Journal on Matrix Analysis and Applications
On computing the eigenvectors of a class of structured matrices
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
In many engineering applications it is required to compute the dominant subspace of a matrix A of dimension mxn, 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 leading to a singular value decomposition-based compression [S. Chandrasekaran, B.S. Manjunath, Y.F. Wang, J. Winkeler, H. Zhang, An eigenspace update algorithm for image analysis, Graphical Models and Image Process. 59 (5) (1997) 321-332]. 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 [P. Van Dooren, Gramian based model reduction of large-scale dynamical systems, in: Numerical Analysis 1999, Chapman & Hall, CRC Press, London, Boca Raton, FL, 2000, pp. 231-247]. In this paper an algorithm for computing an approximation of the left dominant subspace of size k of A@?R^m^x^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.