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Linear Algebra Anyone

Lyle J. Borg-Graham lyle at substantia-nigra.ai.mit.edu
Sun May 17 13:05:47 EST 1992

In article <1992May16.170522.25590 at news.arc.nasa.gov> doshay at ursa.arc.nasa.gov (David Doshay) writes:
>You mention large dense matrix problems. I do compartmental modeling
>(the rest of the world calls it finite element) of neurons here at
>NASA. The matrix is square, the number of compartments on a side.
>We are doing a few thousand now, but are ramping up toward larger
>systems. The big difference is that my matrix is quite sparse. When
>the elements are in an unbranched cable, the system is tri-diagonal,
>but branches make for complications. We also have 2d tissue connecting
>to 1d cables, and that causes large departures from tri-diagonal.
>David		doshay at ursa.arc.nasa.gov

Hines (Efficient computation of branched nerve equations, Int. J.
Bio-Medical Computing, 1984, V.15, pp.69-76) describes an elegant
reordering of nodes for branched (tree) topologies that transform the
general sparse matrix into a tri-diagonal one. Several neuron
simulators that I am aware of use this technique (including one in
Lisp that I use). This technique is also discussed by Mascagni
(Numerical Methods for Neuronal Modeling, Chapter 13 in Methods in
Neuronal Modeling, MIT Press/Bradford Books, 1989, ed. Koch and

Lyle Borg-Graham
Center for Biological Information Processing

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