报告题目：Geometric Methods for Computing Singular Solutions of Algebraic Problems

报告时间：2022-11-17  09:00 - 12:00

报告人：Prof. Zhonggang Zeng   Northeastern Illinois University

腾讯会议ID：431-608-072

Abstract：Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary equations, the models can be formulated to satisfy four easily verifiable conditions so that the data form complex analytic manifolds on which the solutions maintain their structures and the Lipschitz continuity. When such a problem is given with empirical data, solving the system becomes a least squares problem whose solution uniquely exists and enjoys Lipschitz continuity as long as the data point is in a tubular neighborhood of the manifold. As a result, the singular problem is regularized as a well-posed computational problem.