We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber ...

In general, when a quasi-Newton method is applied to solve a system of nonlinear equations, the quasi-Newton direction is not necessarily a descent direction for the norm function. In this paper, we ...

The new version of AlphaZero discovered a faster way to do matrix multiplication, a core problem in computing that affects thousands of everyday computer tasks. DeepMind has used its board-game ...