Abstract
The Sherman–Morrison–Woodbury formula ([GWS-B7], p. 328) is a recipe for constructing the inverse of a matrix after it has been modified by a low-rank correction. For a matrix of size n ×n that has been so modified, it enables the inverse of this matrix to be updated in time proportional to kn, where k is the rank of the correction, rather than the n 3 time usually necessary to compute the inverse directly. This important fact has enabled a variety of algorithms, from early implementations of the simplex method for linear optimization [29] to algorithms for solving least squares problems when new data arrive.
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Eldén, L., Kilmer, M.E., O’Leary, D.P. (2010). Updating and Downdating Matrix Decompositions. In: Kilmer, M.E., O’Leary, D.P. (eds) G.W. Stewart. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4968-5_5
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DOI: https://doi.org/10.1007/978-0-8176-4968-5_5
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-4967-8
Online ISBN: 978-0-8176-4968-5
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