Solving linear equations in lattice quantum chromodynamics

Two Baylor University researchers have developed a new mathematical algorithm that solves the linear equations of the lattice quantum chromodynamics (Lattice QCD) much faster, marking the first time an effective method has been developed to overcome a problem experienced by all Lattice QCD researchers.

In physics, Lattice QCD is a theory of quarks and gluons formulated and solved on a finite space-time lattice of points, however the process of solving millions of linear equations is slowed due to small eigenvalues in the matrix. Eigenvalues help determine energy levels of atoms and how buildings vibrate, but they also determine how fast solution methods for linear equations converge. The algorithms created by Dr Ron Morgan and Dr Walter Wilcox, professors at Baylor University, essentially 'throw out' the small eigenvalues, thus speeding up the process.

'I knew these algorithms had potential, but it was very nice to find that they could work well for an important application such as Lattice QCD,' Morgan said. 'Our new methods work at computing eigenvalues at the same time that the linear equations are solved and using them to speed up the convergence. The methods are particularly effective when systems with multiple right-hand sides need to be solved as is the case in Lattice QCD.'

'It seems the bigger the problem, the better it works,' Wilcox said. 'These methods are the culmination of a remarkable collaboration between mathematics and physics researchers and we are very pleased with the result. This will allow researchers in my field to do more, at a faster pace.'

The research has appeared in the physics journal Nuclear Physics B and several Society for Industrial and Applied Mathematics journals. Wilcox also presented the research at the International Symposium on Lattice Field Theory, which was hosted by University of Regensburg in Germany.