Path: utzoo!attcan!sobmips!uunet!aplcen!samsung!rex!wuarchive!texbell!nuchat!texhrc!bls
From: bls@texhrc.UUCP (Brian L. Sumner)
Newsgroups: comp.graphics
Subject: Spline coefficients
Keywords: matrix problem, help
Message-ID: <352@texhrc.UUCP>
Date: 16 Nov 89 13:42:23 GMT
Organization: Texaco Houston Res. Cntr Hou, Tx
Lines: 35


I am tring to determine a set of spline coefficients, and to do
so I need to solve the linear system
    Ax = b
where A can be a very large (positive definite?) banded matrix.
This matrix looks like

    [ A B . . . ]
    [ B C D . . ]
    [ . D E F . ]
    [ . . F G H ] 
    [ . . . H I ]

where each of A,B, ... I, is itself a (positive definite?) banded matrix
with the same number of bands, e.g.,

    [ a b . . . ]
    [ b c d . . ]
    [ . d e f . ]
    [ . . f g h ] 
    [ . . . h i ]

where each of a,b, ... , i, is again a positive definite?) banded matrix
with the sme number of bands, ...

The number of levels this continues depends on the dimensionality
of the problem, but in practice will be 1,2,3, or 4.

I do not believe that I should just throw such a matrix into a banded
solver.  The regular structure of this matrix begs for a special (faster)
technique.  If you are aware of a method to attack this problem with
I would appreciate it.

Brian Sumner
...!nuchat!convex!texhrc!bls