Let M be a real tridiagonal matrix of size n greater than or equal to 2. We perfectly know how to solve systems of the form MX = Y with dgttrf followed by dgttrs. Now imagine that I am not interested in solving MX = Y anymore, but rather NX = Y where N = M + u.Tv where u,v are columns vectors of size n and where Tv means "transposed of v". Solving NX = Y is equivalent to solve MX = Y, MX = u and MX = v, and is "almost" not more expensive than solving MX = Y when the rank of the matrix u.Tv is small wrt n. (In my case this rank is inferior or equal to 2.)
This is due to the Sherman Morrisson formula, see here -->
My question is : as far as I saw in MKL's documentation, there's no dedicated function doing this Sherman Morrisson trick : am I wrong or not ? Is there other function allowing me to solve system where the matrix defining the system is close to a tridiagonal matrix.
(If not, obviously I could then use dgttrf followed by a dgttrs with a three column matrix for the right hand side, obtained by putting X, u, v together.)
By close, I mean that there existe a tridiagonal matrix such that the difference between the matrix defining the system and this matrix is 1) a matrix of very small rank 2) and matrix with a very small number of non zero entries.