Zhang Neural Networks for Fast and Accurate Computations of the Field of Values

2019/04/23 by Uhlig, Frank · 2 citations
#15A18 #15A60 #65F15 #65F30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1904.10568

Abstract

In this paper a new and different neural network, called Zhang Neural Network (ZNN) is appropriated from discrete time-varying matrix problems and applied to the angle parameter-varying matrix field of values (FoV) problem. This problem acts as a test bed for newly discovered convergent 1-step ahead finite difference formulas of high truncation orders. The ZNN method that uses a look-ahead finite difference scheme of error order 6 gives us 15+ accurate digits of the FoV boundary in record time when applied to hermitean matrix flows A(t).

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