Jianlin Xia

Jianlin Xia is a Professor of Mathematics at Purdue University, with a courtesy appointment in the Department of Computer Science. He joined the university in 2014. Xia holds a Ph.D. in Applied Mathematics from the University of California, Berkeley (2006). His research focuses on numerical linear algebra, fast algorithms for structured matrices, and their applications in computational science and engineering. His work addresses challenges in solving large-scale linear systems, eigenvalue problems, and partial differential equations (PDEs) using innovative methods like fast multipole techniques, hierarchical structures, and randomized algorithms.

Key areas of research include:

• Design and analysis of fast algorithms for structured matrices (e.g., hierarchical, semiseparable, Cauchy matrices)
• Efficient direct and iterative solvers for PDEs, especially Helmholtz equations in seismic modeling
• Stability and robustness of numerical methods in high-performance computing
• Applications in wave propagation, inverse problems, and machine learning

Xia’s contributions include advancements in low-rank approximations, divide-and-conquer eigenvalue decomposition, and scalable preconditioning techniques. His work emphasizes both theoretical analysis and practical implementation, often leveraging parallel computing architectures. Contact: xiaj@purdue.edu.