This question was original posted on SO but it was suggested that I post it here.I'm working on a program in which I have a banded matrix M and a vector b, and I want to maintain an approximate solution vector x such that Mx b. Is there a speedy algorithm or way of modeling this so that I can change individual elements of M and correspondingly update x, without having to do a full matrix inversion?One thing I'm considering is maintaining an approximate inverse of M, using the Sherman Morrison Algorithm in combination with a fast approximate matrix multiplication algorithm like this.
Updating an approximate solution to a linear system in response to a small change
algorithms;linear solver;matrix;approximation algorithms