报告人：潘珺珺 教授
报告题目：QuatIca: Advanced Numerical Linear Algebra and Optimization for Quaternionic Matrices in Python
报告时间：2026年7月16日（周四）下午2：30 - 5：30
报告地点：云龙校区智华楼402室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
Dr. Pan currently is a research assistant professor at Hong Kong Baptist University. Her research interests mainly focus on numerical algorithms and their applications in data science. She has published several papers in journals like SIMAX, SISC, SIIMS, TPAMI, Neural Networks, etc.
报告摘要：
Quaternion-valued representations provide a convenient way to model coupled multi-channel signals (e.g., RGB imagery, polarization data, vector fields, and multi-detector time series). Yet practical and numerically reliable software support remains far less mature than those based on the real/complex setting. Here, we present QuatIca, an open-source Python library for quaternion numerical linear algebra and optimization, designed for both research prototyping and reproducible experimentation. QuatIca provides core quaternion matrix operations and norms; dense decompositions and reductions (QR, LU, Q-SVD, eigendecomposition, Hessenberg/tridiagonal reduction, Cholesky decomposition, and Schur helpers); iterative solvers including quaternion GMRES (with preconditioning) and Newton-Schulz pseudoinverse schemes; and domain-focused routines for signal and image processing such as quaternion Tikhonov restoration. The library also includes OptiQ, which solves quaternion Hermitian semidefinite programs using log-det barrier Newton methods with -continuation. We highlight design choices that preserve quaternion structure, and we provide end-to-end demonstrations including quaternion image deblurring, Lorenz-attractor filtering, and quaternion image completion. QuatIca is distributed via PyPI and accompanied by open-source development on GitHub and continuously deployed documentation with runnable tutorials.