Estimating Effective Capacity in Erlang Loss Systems under Competition
Queueing Systems: Theory and Applications
Computing estimates of continuous time macroeconometric models on the basis of discrete data
Computational Statistics & Data Analysis
Exponential natural evolution strategies
Proceedings of the 12th annual conference on Genetic and evolutionary computation
An Efficient Method for Modeling Kinetic Behavior of Channel Proteins in Cardiomyocytes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Collision-free and smooth trajectory computation in cluttered environments
International Journal of Robotics Research
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Matrix exponentials and their derivatives play an important role in the perturbation analysis, control, and parameter estimation of linear dynamical systems. The well-known integral representation of the derivative of the matrix exponential exp(tA) in the direction V, namely @!^t"0exp((t - @t)A)V exp(@tA) d@t, enables us to derive a number of new properties for it, along with spectral, series, and exact representations. Many of these results extend to arbitrary analytic functions of a matrix argument, for which we have also derived a simple relation between the gradients of their entries and the directional derivatives in the elementary directions. Based on these results, we construct and optimize two new algorithms for computing the directional derivative. We have also developed a new algorithm for computing the matrix exponential that is more efficient than direct Pade approximation, which is based on a rational representation of the exponential in terms of the hyperbolic function A coth(A). Finally, these results are illustrated by an application to a biologically important parameter estimation problem which arises in nuclear magnetic resonance spectroscopy.