Methods for Updating the Singular Value Decomposition
DOI:
https://doi.org/10.7146/dpb.v3i26.6445Abstract
The linear least squares problem of minimizing ||Ax~ - b~||_(2) where A is an m X n matrix, m >= n, may be solved using the singular value decomposition in approximately 2mn^(3) + 4n^(3) multiplications. In this paper the problem of solving ||A'x~ - b~||_(2) is considered where A' results from deleting or adding a column to A. This might occur when a change is made in the model of a process. Instead of computing the singular value decomposition of A' from scratch, the singular value decomposition of A is updated. Since the updating require about 6n^(3) multiplications the algorithms are useful when m >> n. The problem of recalculation some or all of the singular values of a matrix A', which is obtained by deleting or adding a row or a column from a matrix A, whose singular value decomposition is known, is also studied.Downloads
Published
1974-03-01
How to Cite
Kaufman, L. (1974). Methods for Updating the Singular Value Decomposition. DAIMI Report Series, 3(26). https://doi.org/10.7146/dpb.v3i26.6445
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Articles published in DAIMI PB are licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.