演講者：李宗錂博士

單　位：Michigan State University

日　期：2009年7月17日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Computing the Numerical Rank of Large Matrices 

摘　要：

If rank deficiency for a large matrix is known to be small apriori, there seems no need to compute SVD to find all singular values for determining its rank. While the Householder QR with column pivoting algorithm proposed by Golub and Businger in 1965works quite well I general for this purpose, there exist counter examples (by W. Kahan) that the method would fail. These failures of this sort had been overcome by T. Chan’s RRQR algorithm in 1989. In practice, such as in signal processing, rank updatings and downdatings occur commonly along with the rank-revealing. While the UTV decomposition method for rank reveling proposed by G. W. Stewart in 1992 works quite well in rank updatings, it may not be efficient for the downdatings. Recently, an efficient algorithm for rank revealing is proposed by T. Y. Li and Z. Zeng. For the method, both updatings and downdatings become quite straightforward. The related results will also be presented in this rank.