The contact mode high-speed atomic force microscope (AFM) operates orders of magnitude faster than conventional AFMs. It is capable capturing multiple frames per second with nanometre-scale lateral resolution and subatomic height resolution. This advancement in imaging rate allows for microscale analysis across macroscale surfaces, making it suitable applications materials science. However, the...

We present two sampled quasi-Newton methods (sampled LBFGS and LSR1) for solving empirical risk minimization problems that arise in machine learning. Contrary to the classical variants of these sequentially build Hessian or inverse approximations as optimization progresses, our proposed sample points randomly around current iterate at every iteration produce approximations. As a result, constru...