Rate My Professor Ren-Cang Li

Li's research focuses on numerical linear algebra, including perturbation theory for eigenvalues and singular values, numerical solutions of ordinary differential equations, scientific computing, high performance computing, reduced order modeling, and data science areas such as online algorithms, dimensionality reduction, nonlinear manifold learning, and compressed sensing. He has published over 138 journal articles, one book—"Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations" with Tsung-Ming Huang and Wen-Wei Lin (SIAM, 2018)—and a chapter "Matrix Perturbation Theory" in the Handbook of Linear Algebra (2007, revised 2014). Key papers include "Relative perturbation theory: I. Eigenvalue and singular value variations" (SIAM Journal on Matrix Analysis and Applications, 1998), "Relative perturbation theory: II. Eigenspace and singular subspace variations" (1999), "First-order perturbation theory for eigenvalues and eigenvectors" with Anne Greenbaum and Michael L. Overton (SIAM Review, 2020), and contributions to "Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide" (2000). Li has served as Associate Editor for SIAM Journal on Matrix Analysis and Applications (2006-2012), Numerical Algebra, Control and Optimization (2011-2017), Taiwanese Journal of Mathematics (2017-), and others. He has advised multiple PhD students and teaches graduate courses in numerical analysis.