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講題: Rank revealing, updating, and downdating problems
演講者：李宗錂 教授(國立中山大學應用數學系)
Abstract:The rank revealing problem arises widely in scientific computing and engineering applications, such as signal processing, information retrieval, numerical polynomial algebra, and so on. Some of those applications give rise to a large matrix whose rank or nullity is known to be small apriori. Although the Golub-Reinsch SVD algorithm can be applied to calculate all singular values and hence determine numerical rank, it becomes unnecessarily expensive in these situations. Furthermore, it is relatively difficult to update the SVD when the matrix is altered by inserting or removing a few rows or columns. Several alternative methods have been proposed as alternatives for this purpose. In general, they compute a gap-revealing factorization for estimating the singular values. Recently we proposed two new rank-revealing methods to deal with large matrices with high ranks and low ranks respectively. Rather than computing a gap-revealing factorization, our methods construct an orthonormal basis for the numerical subspace of the matrix directly. The resulting algorithms are quite efficient, and they only output those numerical subspaces that are usually in demand in real applications. For the new methods, the corresponding updating and downdating algorithms become quite straightforward.
時間：2010年10月22日(星期五) 10：30 ∼ 11：30
地點：推廣大樓3樓9313室
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