A New Real Structure-Preserving Quaternion QR Algorithm with Application to Color Image Watermarking
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：贾志刚教授
：2019-11-24 16:00
：实验楼105
Speaker：Prof. Zhigang Jia
Jiangsu Normal University
Title: A New Real Structure-Preserving Quaternion QR Algorithm with Application to Color Image Watermarking
Time：24 Nov 2019, 16:00
Location：实验楼105
Abstract: In this talk, new real structure-preserving decompositions are introduced to develop fast robust algorithms for the (right) eigenproblem of general quaternion matrices. Under the orthogonally JRS-symplectic transformations, the Francis JRS-QR step the JRS-QR algorithm are firstly proposed for JRS-symmetric matrices then applied to calculate the Schur form of quaternion matrices. A novel quaternion Givens matrix is defined utilized to compute the QR factorization of quaternion Hessenberg matrices. An implicit double shift quaternion QR algorithm is presented with a technique for automatically choosing shifts within real operations. The quaternion QR algorithm is applied to the color image watermarking. Numerical experiments are provided to demonstrate the efficiency accuracy of newly proposed algorithms.
Speaker Introduction：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. Imaging Sci., J. Sci. Comput., Numer. Linear Algebra Appl.等国际知名期刊上发表学术论文30余篇，出版译著1部、教材1部，主持国家自然科学基金项目2项、省部级科研项目1项，参加国家和省自然科学项目4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。曾经到英国曼彻斯特大学、香港浸会大学等高校数学系进行为期一年的访问。现兼职为中国高等教育学会教育数学专业委员会团体理事、江苏省工业与应用数学会理事、江苏省计算数学学会理事、美国SIAM正式会员，美国Math Review评论员，和SIMAX，Inverse Problem，Automatic等学术期刊的审稿人。
联系人：白正简教授
