The name is absent

31

goal is to reduce the dimension of this system while exactly preserving the inputs and
without sacrificing the accuracy of the soma potential.

2.4 Linear Model Reduction Techniques

I have used two different techniques for linear model reduction. One technique is
the classical time-domain method known as Balanced Truncation (ВТ), which enjoys
rigorous theoretical grounding and error analysis but which generally requires dense
matrix computations. To combat the computational cost associated with this, I use
a newer frequency-domain approach called the Iterative Rational Krylov Algorithm
(IRKA). This method achieves essentially the same accuracy as BT in practice, but
with an increase in speed of orders of magnitude, thus providing an efficient and
accurate algorithm for model reduction of quasi-active systems.

2.4.1 Balanced Truncation

To balance a linear dynamical system is to transform it into one where the
controllability and observability gramians coincide. As a result, and in a rigorous
quantitative sense, the states that are difficult to reach are rarely observed. We
present the method below. For the early history, and further details and applications,
see (Moore, 1981), (Kailath, 1980), (Antoulas and Sorensen, 2001), and (Antoulas,
2005).

<<   38   39   40   41   42   43   44   >>

More intriguing information