Abstract
Let {A k } k=1 p , , be a sequence of m × k matrices such that A k+1 is obtained from A k by appending a column. In this paper a lower bound δ k+1 for the least singular value of each matrix A k+1 is derived from the value δ k . The kth step of the algorithm is based on the solution of the least squares problem A k x k =b k , using the QR updating scheme, so that the algorithm requires O(mp 2 + p 3) operations. Lastly, an error analysis is performed in order to detect when the computed lower bound is a good approximation of the exact least singular value.
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