DMS Algebra/Linear Algebra Seminar

Speaker: Frank Uhlig

Title: Time-varying Matrix Numerics, Zhang Neural Networks, and an Intractable Static Matrix Problem, Finally Solved

Abstract: This talk introduces predictive Zeroing Neural Networks or Zhang Neural Networks (ZNN) for time-varying matrix computations. These neural networks were invented 20 years ago by Yunong Zhang and his advisor Juan Wang at Chinese University in Hong Kong and they have been widely used in engineering since then for robots, for autonomous vehicles, and in many other applications. The engineering literature contains over 300 papers on ZNN and on recurring neural networks (RNN). There are 5+/- books on the subject. The ZNN or RNN methods have never been studied by Numerical Analysts. Here we explain their inner workings and their numerical behavior which differs greatly for our now classic knowledge of static matrix problems. To illustrate, we study matrix field of values (FoV) computations and solve the previously intractable FoV problem for decomposable matrices A when trying to use path following methods.