报告时间：2022年4月12日  14:30

地 点：线上腾讯会议 430-917-122

报告人：  贾志刚（江苏师范大学）

报告题目：Structure Preserving Quaternion Generalized Minimal Residual Method and Application to Color Image Deblurring

汇报摘要：

In this talk, we mainly develop the quaternion generalized minimal residual method (QGMRES) for solving quaternion linear systems. Quaternion linear systems arise from three-dimensional or color imaging filtering problems. The proposed quaternion Arnoldi procedure can preserve quaternion Hessenberg form during the iterations. The main advantage is that the storage of the proposed iterative method can be reduced by comparing with the Hessenberg form constructed by the classical GMRES iterations for the real representation of quaternion linear systems. The convergence of the proposed QGMRES is also established. QGMRES is also applied to solve color image deblurring problem. Numerical examples are presented to demonstrate the effectiveness of the proposed QGMRES compared with the traditional GMRES in terms of storage and computing time.

汇报人简介：

贾志刚 ，江苏师范大学教授、硕士生导师。2009年毕业于华东师范大学数学系，获理学博士学位。主要研究方向为数值代数与图像处理，至今已在SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., SIAM J. Imaging Sci., J. Sci. Comput., Numer. Linear Algebra Appl.等国际知名期刊上发表学术论文40余篇，在科学出版社出版专著和译著各1部，主持国家自然科学基金项目3项、省高校自然科学研究重大项目1项，参加国家自然科学基金重大项目1项。先后入选江苏师范大学“第一批高层次人才队伍后备人选”、“三育人先进个人”、“校先进工作者”等。曾先后到英国曼彻斯特大学、香港浸会大学、澳门大学等高校数学系进行学术访问。现兼职为中国高等教育学会教育数学专业委员会常务理事、江苏省计算数学学会理事、美国Math Review评论员等，同时为SIMAX，SISC, SSIMS, Inverse Problem，Automatic，JCAM, IEEE TSP，Signal Processing等学术期刊的审稿人。