One day, my officemate Tieming asked me about a problem that she met in her research. Suppose \(\boldsymbol{B}\) is a symmetric matrix of huge dimension and \(\boldsymbol{D}\) is a diagonal matrix with nonnegative diagonal elements. The inverse of \(\boldsymbol{B}\) is already known, how can we calculate the inverse of \(\boldsymbol{B}+\boldsymbol{D}\) efficiently? I thought for a while and found a good way to solve the problem. See solution in Inverse of Matrix.

I haven't implemented the algorithm yet, but a roughly estimate of the complexity of this algorithm tells me that even R can handle it. I will write a R function to do this later when I have time.