The Block Lanczos Iteration for Functional Trace Estimation

Matthew Louis / December 2024

This Fall I got the chance to take a course on iterative methods (MATH 6644). I was finally able to rigorously learn about Krylov subspace methods (and projection methods in general), and the class culminated with geometric multigrid methods for elliptic PDEs, which might just be the coolest class of iterative solvers I’ve learned about.

For a class project, me and my partner Shrikanth investigated block Krylov subspace methods for preconditioning stochastic quadratures used for computing trace estimators. We couldn’t find a stong business case for the block preconditioners on the test matrix we used (and with our reorthogonalization scheme), but there’s probably more work to be done to say that it’s not useful for any problem.

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