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Does there exist a fast way to calculate the inverse of an $N \times N$ matrix, if we know the inverse of the $(N-1) \times (N-1)$ sub-matrix?

For example, if $A$ is a $1000 \times 1000$ invertible matrix for which the inverse is known, and $B$ is a $1001 \times 1001$ matrix obtained by adding a new row and column to $A$, what is the best approach for calculating inverse of $B$?

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What if $B$ and $B^{-1}$ were known and $A^{-1}$ was needed ? – mghandi Mar 21 '11 at 21:53
up vote 10 down vote accepted

Blockwise inverse

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