Numerical Analysis of Matrix Rank Deficiency

Zhonggang Zeng
Northeastern Illinois University
Professor of Mathematics

“Rank deficient matrices are frequently encountered and often dreadful in scientific computing, but rarely elaborated in numerical analysis textbooks. Accurate solutions of problems involving such matrices are known to be difficult for being highly sensitive to data perturbations and round-off. On the other hand, it is also known that the hypersensitivity of matrix rank is one-directional: Tiny perturbations can only increase the rank and never decrease it. In geometric terms, matrices of the same rank form a complex analytic manifold that is embedded in manifolds of lower  codimensions. This characteristic is crucial in numerical analysis and in forming computational  strategies. Many problems that are perceived to be  ill-conditioned can be regularized so that the high sensitivities become manageable or even eliminated. In this talk we shall elaborate the essence of numerical rank, the numerical rank-revealing problem and regularization of singular linear systems along with algorithms, software and applications”.

Light refreshments will be served @ 1:30pm EMS E424A.

View Zeng’s Event Flyer