I want to get the math behind of the Rayleigh-Ritz Procedure (that minimize Rayleigh quotient) But when I look at the code (*), I cannot understand: Why are Gram matrices in the Rayleigh-Ritz procedure constructed this way? And why we should solve the eigenproblem with Gram matrices?
Can someone explain why we use Gram matrices or advice a paper that covers this? I googled but didn't find any description of the Gram matrix into Rayleigh-Ritz
- the pseudocode I mentioned before is a part of LOBPCG algorithm (page 5) https://arxiv.org/pdf/0705.2626.pdf
Thank you in advance