Speaker
Description
Estimating the trace of the inverse of a large quark matrix is a longstanding problem in lattice QCD. Hutchinson's method is the standard for this calculation, which uses random noise vectors to achieve a desired tolerance. Doing so requires solving a system of linear equations $Ax = b$, where $b$ is the random noise vector. In this work, we introduce novel solving algorithms for use in Hutchinson's method: Non-symmetric Lanczos, Twin BiCG, and Twin BiCGStab. On the whole, these algorithms benefit from fewer matrix vector products per iteration and are very naturally adapted to large-scale GPU and other distributed HPC environments. These algorithms are tested on variable size lattice QCD matrices and in various computing contexts. The first part of this talk will highlight the solver methods and interpret testing results. The second part of this talk will discuss how these methods stand in service of a more sophisticated evaluation of $Tr(A^{-1})$ which implements a polynomial approximation of $A^{-1}$ and a singular value deflation.