Zhang Neural Networks for Fast and Accurate Computations of the Field of Values
For researchers needing fast and accurate FoV computations, this work provides a novel neural network approach with high precision, though it is incremental in adapting existing ZNN methods.
The paper applies Zhang Neural Networks (ZNN) with high-order finite difference formulas to compute the field of values (FoV) for Hermitian matrix flows, achieving 15+ accurate digits of the FoV boundary in record time.
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 $A(t)$.