re: BIRD29 Name for new banded matrix structure

To IBIS team and commentors:

I believe the need for a revised matrix structure which utilizes the "banding"
format efficiency is apparent and not being debated.

Two issues are emerging:

(1) Do we really require another alternative keyword to support "banding"
with no end-to-end coupling and "banding" with end-to-end coupling. I
would hope not because the original banding method does have the technical
format restriction which the revised method would overcome and serve
as the proper method. I would hope that any existing implementations
could be updated at the "next release" to make the revised version
of banding the standard way.

(2) The second issue concerns terminology. I believe the existing
terminology can also be used for the revised structure by thinking in
terms of an augmented matrix structure as Bob Ward and Chris Reid have
mentioned:

To paraphrase from MATRIX COMPUTATIONS by Golub and Van Loan, pg. 6,
"We say that an N x M matrix A has a lower bandwidth of r and an upper
bandwidth of s if a(i,j) = 0 whenever i > j + r and j > i + s. If r = s,
then A is simply said to have bandwidth r."

For package model descriptions what we really want is the matrix of the
form Eric presented:

           1 2 3 4 5 6 7 8

       1 X X X X X
       2 X X X X X
       3 X X X X X
       4 X X X X X
       5 X X X X X
       6 X X X X X
       7 X X X X X
       8 X X X X X

By augmenting the matrix (by repeating columns 1...B) we enter only the upper
triangle data corresponding to this:

           1 2 3 4 5 6 7 8 1 2

       1 X X X
       2 X X X
       3 X X X
       4 X X X
       5 X X X
       6 X X X
       7 X X X
       8 X X X

Because a(i,j) = a(j,i), we have from this format all of the information needed
to populate the original N x N matrix. Furthermore, this is really a
Banded_matrix according to the definition for an N x M matrix when filling
in the implied lower-triangle terms which did not need to be entered:

           1 2 3 4 5 6 7 8 1 2

       1 X X X
       2 X X X X
       3 X X X X X
       4 X X X X X
       5 X X X X X
       6 X X X X X
       7 X X X X X
       8 X X X X X

So my preference would be to stay with the three matrix formats, but to
update the definition.

Bob Ross,
Interconnectix, Inc.
Received on Thu Jun 1 10:12:11 1995