报告题目：One-Pass Randomized Algorithm with Practical Rangefinder for Low-Rank Approximation to Quaternion Matrices

报 告 人：杨宇宁 教授

报告地点：腾讯会议650437708

报告时间：2024年5月25日20:00-21:00

报告摘要： As its real/complex counterparts, randomized algorithms for low-rank approximation to quaternion matrices received attention recently. For large-scale problems, however, existing quaternion orthogonalization methods are not efficient, leading to slow   rangefinders. By possibly relaxing orthonormality while maintaining favaroable condition numbers, this work proposes two practical quaternion rangefinders that take advantage of mature scientific computing libraries to accelerate heavy computations.

They are then incorporated into the quaternion version of a well-known one-pass algorithm. Theoretically, we establish the  probabilistic error bound,  and demonstrate that the   error is proportional to the condition number of the rangefinder. Besides  Gaussian, we also allow  quaternion sub-Gaussian test matrices.  Key to the latter is the derivation of a deviation bound for extreme singular values of a quaternion sub-Gaussian matrix. Numerical experiments indicate that the one-pass algorithm with the proposed rangefinders work efficiently while only sacrificing little accuracy. In addition, we tested the   algorithm in an on-the-fly 3D Navier-Stokes equation data compression to demonstrate its efficiency in large-scale applications.

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）。现担任中国运筹学会数学规划分会青年理事，中国工业与应用数学学会理事，广西运筹学会理事，广西大学学术委员会委员。