Structured backward error analysis for (generalized) saddle point problems

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:2022-04-16 09:00


时  间:416日下午09:00

地  点:腾讯会议ID507663044(无密码)


Recently, the structured backward errors for the generalized saddle point problems with some different structures have been studied by some authors, but their results involve some Kronecker products, the vec-permutation matrices and the orthogonal projection of a large block matrix which make them very expensive to compute when utilized for testing the stability of a practical algorithm or as an effective stopping criteria. In this paper, adopting a new technique, we present the explicit and computable formulae of the normwise structured backward errors for the generalized saddle point problems with five different structures. Our analysis can be viewed as a unified or general treatment for the structured backward errors for all kinds of saddle point problems and the derived results also can be seen as the generalizations of the existing ones for standard saddle point problems, including some KKT systems. Some numerical experiments are performed to illustrate that our results can be easily used to test the stability of practical algorithms when applied some physical problems. We also show that the normwise structured and unstructured backward errors can be arbitrarily far apart in some certain cases.


郑兵,兰州大学数学与统计学院教授、博士生导师。长期从事数值代数、神经网络算法的研究工作,负责承担国家自然科学基金面上项目、教育部外国专家重点项目、甘肃省自然科学基金项目等10余项。 多次应邀赴美国、日本、西班牙、俄罗斯、印度以及香港、澳门等国家和地区参加学术会议并做学术报告,并先后在印度统计研究所新德里中心和美国Emory大学数学与计算机科学系做访问学者。迄今已在《SIAM J. Matrix Anal. Appl., J. Math. Anal. Appl.J. Optim. Theory Appl., Linear Algebra Appl.》,《J. Multivariate Anal.》,《Adv. Comput. Math.》, Numer. Linear Algebra Appl.》, IEEE Trans. Neural Netw. Learn. Syst. 以及《Automatica》等国内外重要刊物上发表论文百余篇。2005年荣获甘肃省第十二届高校青年教师成才奖。