勷勤数学•专家报告

题      目：Accurate Restricted Singular Value Decomposition via Deflation on Neville Representations

报  告  人： 黄荣 教授  (邀请人：黎稳)

                                    湖南师范大学

时      间： 5月29日  10：30-11:30

地     点：数科院东楼401

报告人简介:

        黄荣，教授、博士生导师，湖南省芙蓉学者奖励计划获得者、湖南省杰出青年基金获得者、湖南省普通高校学科带头人等。主要从事数值代数研究工作，以独立完成人身份获得湖南省自然科学奖二等奖1项，以及主持获得湖南省高等教育教学成果奖二等奖1项，先后主持完成国家自然科学基金面上项目/青年项目、教育部博士点基金、湖南省杰出青年基金等，研究成果全部以独著或第一作者方式发表在Math. Comp.、SIAM. J. Matrix Anal. Appl.、J. Sci. Comput.、Adv. Comp. Math.等。

摘      要：

       This talk introduces a deflation method for accurately computing the restricted singular value decomposition (RSVD) of a matrix triplet using its Neville representations (NRs).  Our method exactly extracts all non-regular restricted singular values (RSVs) and deflates the triplet into a regular form while maintaining numerical accuracy. This approach ensures that all nonzero RSVs are computed with high relative accuracy, and all zero RSVs are exactly identified. It also exactly determines the dimensions of the associated nullspaces and their intersections. We establish rigorous perturbation bounds, demonstrating that the RSVD is accurately governed by its NR elements. The derived relative error bounds guarantee the high accuracy for the computed RSVD. Numerical experiments validate the claimed high relative accuracy.

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