Hi everyone, I need to solve a linear system Ax=b where A is a 1000x1000, 99% sparse matrix with the following particular structure: A=I - beta Q, where beta<1 but close to 1 (eg 0.995) and Q is a sparse Markov transition matrix (all coefficients 0<q<1, rows sum to one). What would be a good way to approach this? I have tried direct factorization methods as well as the various lsqr() methods available in Julia packages, treating A as any other sparse matrix, but was not successful. Do you know of any method that would leverage the particular structure of A? Alternatively, what might be good options to try with methods such as lsqr(), for instance what type of preconditoning, etc.?
Thank you. Ben
