A fast algorithm for the recursive calculation of dominant singular subspaces
- 作者：N. Mastronardi ; M. Van Barel ; R. V ; ebril
- 关键词：Householder matrix ; Givens rotation ; URV factorization ; Updating ; Singular value decomposition
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2008
- 期刊代码：72_03770427
- 类别：cp
- 出版时间：1 September 2008
- 卷：218
- 期：2
- 页码：238-246
- 文件大小：412 K
摘要
In many engineering applications it is required to compute the dominant subspace of a matrix A of dimension me="mml103">method=retrieve&_udi=B6TYH-4N3GFH7-1&_mathId=mml103&_user=1067359&_cdi=5619&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=94002a9231b08902772c4d692cf7d4dc" title="Click to view the MathML source" alt="Click to view the MathML source">m×n, with me="mml104">method=retrieve&_udi=B6TYH-4N3GFH7-1&_mathId=mml104&_user=1067359&_cdi=5619&_rdoc=6&_acct=C000050221&_version=1&_userid=10&md5=8c9ef96e5b379eb02424d8379e04b591" title="Click to view the MathML source" alt="Click to view the MathML source">mmg src="http://www.sciencedirect.com/scidirimg/entities/2aa2.gif" alt="not double greater-than sign" title="not double greater-than sign" border="0">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].