Updating the inverse of a matrix

16-Feb-2020 23:48

Perhaps you are looking for the Sherman-Morrison-Woodbury update, which allows to perform a rank k update directly to the inverse of a matrix rather than inverting a rank k update to the matrix itself.

It is used heavily in statistics and optimization literature.

The key insight is that one way to compute the SSCP matrix is as a sum of outer products of the rows of X.

Therefore if x`) The formula shows how to compute the inverse of the updated SSCP by using a matrix-vector multiplication and an outer product.

updating the inverse of a matrix-52

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Imagine doing linear regression, but being given the datapoints one-by-one.

The following program creates a new design matrix (Z) that excludes the row, forms the new SSCP matrix, and finds its inverse: similar computations.

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