26 citations · 28 across the 9 of their papers we have counts for
7 papers · 1 filter
The Eight Epochs of Math as regards past and future Matrix Computation
Frank Uhlig
This paper gives a personal assessment of Epoch making advances in Matrix Computations from antiquity and with an eye towards tomorrow. We trace the development of number systems a…
Constructing the Field of Values of Decomposable and General Matrices Using the ZNN Based Path Following Method
Frank Uhlig
This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve for every conceivable complex or real square matrix…
On the Block-Decomposability of 1-Parameter Matrix Flows and Static Matrices
Frank Uhlig
For general complex or real 1-parameter matrix flows and for time-invariant static matrices $A \in \CC_{n,n}$ alike, this paper considers ways to decompose matrix flow…
Coalescing Eigenvalues and Crossing Eigencurves of 1-Parameter Matrix Flows
Frank Uhlig
We investigate the eigenvalue curves of 1-parameter hermitean and general complex or real matrix flows in light of their geometry and the uniform decomposability of f…
The Construction of High Order Convergent Look-Ahead Finite Difference Formulas for Zhang Neural Networks
Frank Uhlig
Zhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer…
Zhang Neural Networks for Fast and Accurate Computations of the Field of Values
Frank Uhlig
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-va…
Time-Varying Matrix Eigenanalyses via Zhang Neural Networks and look-Ahead Finite Difference Equations
Frank Uhlig, Yunong Zhang
This paper adapts look-ahead and backward finite difference formulas to compute future eigenvectors and eigenvalues of piecewise smooth time-varying symmetric matrix flows .…