LOBPCG Initial k eigenvectors approximation

Hello,

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?

Thank you,

Frank

Answer 1

[Andrew Knyazev]

See https://en.wikipedia.org/wiki/LOBPCG#Convergence_theory_and_practice