报告标题: One-Pass Randomized Algorithm with Practical Rangefinder for Large-Scale   Quaternion Matrix Approximation

报告人：杨宇宁，(广西大学数学与信息科学学院 教授)

报告摘要:   Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthogonalization methods are inefficient, leading to slow rangefinders. To address this, by taking advantage of mature scientific computing libraries to accelerate heavy computations, this work devises two practical quaternion rangefinders, one of which is allowed to be non-orthonormal yet well-conditioned. They are then integrated into the quaternion version of an existing one-pass algorithm, which originally takes orthonormal rangefinders only. We establish the error bounds and demonstrate that the error is proportional to the rangefinder's condition number. The probabilistic bounds are exhibited for both quaternion Gaussian and sub-Gaussian embeddings. Numerical experiments demonstrate that the one-pass algorithm with the proposed rangefinders significantly outperforms previous techniques in efficiency. Additionally, we tested the algorithm in a 3D Navier-Stokes equation ($5.22$GB) and a 4D Lorenz-type chaotic system ($5.74$GB) data compression, as well as a $31365\times 27125$ image compression to demonstrate its efficiency in large-scale applications.

报告时间：2024年6月1日  (周六)15：00-16：30

报告地点：六教南528

报告人简介：杨宇宁，2003至2013年本硕博就读及毕业于南开大学数学科学学院。2013至2017年于比利时鲁汶大学从事博士后研究。2017年入职广西大学数学与信息科学学院。2018年入选国家级人才青年项目，同年任教授。研究领域为张量计算和优化。总计发表SCI论文40余篇，发表期刊包括SIAMJ.Optim., SIAMJ.Matrix, Anal.Appl., J.Mach.Learn.Res., IEEETrans.NeuralNetw.Learn.Syst.等。著专著一部。主持国家自然科学基金面上基金、青年基金（已结题）、霍英东青年教师基金（已结题）。