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Linear Algebra Anyone

Lyle J. Borg-Graham lyle at substantia-nigra.ai.mit.edu
Tue May 19 12:05:07 EST 1992

     In article <1992May17.233022.9192 at news.arc.nasa.gov> doshay at ursa.arc.nasa.gov (David Doshay) writes:

     >In my case this does not work because the 2d tissue that we also model
     >is not tridiagonal at all, though it can be properly ordered to be strongly
     >diagonally dominant. We could use the Hines method on all the branched
     >cables, using other methods when we do the 2d tissue, but at this point
     >we are using a sparce matrix solver that is relatively fast without adding
     >the complication of using 2 different methods for different parts of the 
     >total matrix. We will probably add a preconditioner, that does what is
     >essentially a generalization of the Hines technique, when our data sets
     >get larger. At this point we have not yet seen that it will speed us up
     >enough to implement it.

You might look into relaxation techniques for solving the matrix -
these require diagonally-dominant matrices which in general is the
case for syncytium or neurons because of the membrane capacitance.
These techniques have been applied to VLSI simulations:

  Author  = {Webber, D. and Sangiovanni-Vincentelli, A.},
  Title   = {Circuit Simulation on the Connection Machine},
  BookTitle  = {Design Automation Conf.},
  Year    = {1987}

	Author = {White, J. and Sangiovanni-Vincentelli, A.},
  Title     = {Relaxation Techniques for the Simulation of VLSI Circuits},
  Publisher = {Kluwer},
  Year      = {1986}


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