Host: Jin-Peng Liu 刘锦鹏

Abstract: Verifying spectral bounds of large sparse non-Hermitian operators is challenging because conventional eigensolvers suffer from high computational cost and severe spectral ill-conditioning. We propose a corrected composite contour (CCC) trace estimator that combines rational approximation of indicator functions with randomized trace estimation. The method accounts for linear-solver, sampling, and rational-approximation errors. A composite contour rule for general piecewise-smooth regions achieves near-machine-precision accuracy, while estimating exterior eigenvalue counts substantially reduces sampling variance. Numerical experiments verify spectral bounds for reciprocal and non-reciprocal systems with matrix dimensions up to 1,250,000 and 785,347, respectively, extending existing capabilities by two to three orders of magnitude. Experiments on a three-dimensional spinful system also identify eigenvalues inside a theoretically predicted spectral hole.

Bio: 李颖洲，复旦大学数学科学学院教授。2012年于复旦大学获学士学位，2017年于美国斯坦福大学获计算数学博士学位，2017年至2020年在美国杜克大学担任科研助理教授。设计算法并分析CNN万有逼近，提出高频波方程深度神经网络结构与训练框架；面向中性原子量子计算机设计高性能量子算法。已在国际顶尖计算数学、应用学科杂志发表论文50余篇。