Updating the inverse of a matrix

Any help, hints, suggestions, or references would be much appreciated!

0$ for $i \in [1, n]$, diag is diagonal matrix, and $P $ is invertible.

This paper suggests certain methodologies to update the given matrix inverse for variation of operating conditions.

updating the inverse of a matrix-54

Thanks to rank-one updates, we can bring that cost down to .

At each step if is the current design matrix, our new datapoint is , then the updated version of is: and so that we have a rank-one update to for each new datapoint.

The update in the existing matrix inverse is usually needed because of changes in one or more elements of the original matrix or a change of one row or one column.

Changes in value of elements of a matrix may occur due to variation in operating conditions of the system.

Existing techniques of matrix inversion do offer the possibility of updating the inverse.