Updating and Downdating Matrix Decompositions
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  to algorithms for solving least squares problems when new data arrive.
KeywordsSingular Vector Cholesky Factor Plane Rotation Signal Subspace Noise Subspace
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