I am currently working with the lobpcg.py code in python to solve for the eigenvalues and eigenvectors of large sparse matrices. I noticed that the solution is quite sensitive to the initial eigenvectors approximations X.
I am currently using a random function to generate the initial approximations and wanted to know if there is a better about doing this. Could I use a fixed X? Which X could I use to ensure that it will work for many different matrices and still converge?