We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on LDLT decomposition, and involves finding a part of the inverse of the original Hankel matrix. The computation involves extremely high precision arithmetic, and both message passing interface and shared memory parallelization. We show that this approach achieves good scalability on a high performance computing cluster, and it is a major improvement of the earlier approaches. We use this method to study a family of Hankel matrices with weight w(x)= that arise in random matrix theory. For the case of β=1/2, we are able to match the conjectured leading exponent to the numerical results.
星期二, 2018/06/26 - 从 14:30 到 16:00
Yang CHEN 教授