Consider calculating the inverse of matrix sum
where A is a symmetric dense matrix while B is a symmetric block diagonal matrix. I am interested in finding an efficient approach to update the inverse of the sum A+B if the values in one of the diagonal blocks of matrix B are multiplied by a real value s.
So my question is equivalent to updating the inverse of
where A and B are defined as above, and K is a diagonal matrix with some diagonal entries (corresponding to one block of B) being s while rest being 1. Is there a possible way for efficient iterative update of matrix inverse (A + B * K)-1 when s is changing?