From: robin <robin_v@bigpond.com>
Subject: Re: Solve a n x n system with tridiagonal matrix method
Date: Fri, 08 Oct 1999 12:59:49 GMT
Newsgroups: sci.math.num-analysis

"Nikos Hatzistelios" <hatzisn@x-treme.gr> writes: > How can I do that ?
> Pls point me to some directions or resources
> or even better answer to me directly or in
> this newsgroup.
> 
> Thanks
> hatzisn@x-treme.gr

There is an example in "Introduction to PL/I, Algorithms, and Structured
Programming" 0-8586384-8-2
with explanation.
==============================================================================

From: rroachJUNK@cvd-pro.com.JUNK
Subject: Re: Solve a n x n system with tridiagonal matrix method
Date: Sun, 10 Oct 1999 08:03:17 GMT
Newsgroups: sci.math.num-analysis

I presume scalar tridiagonal (i.e. each nonzero element is only a 1x1
matrix).  So let the three diagonals be represented by c(i),b(i),a(i)
and let the rhs be represented by d(i) so that the linear system is
given by:

     c(i)*x(i-1) + b(i)*x(i) + a(i)*x(i+1)  = d(i)
 
the array x(i) is the array of unknowns.  Your matrix is nxn, so the
algorithm is:

rem--------- eliminate the c-diagonal -----------------
for i = 1 to n
  cbi = c(i)/b(i-1)
  b(i) = b(i) - cbi*a(i-1)
  d(i) = d(i) - cbi*d(i-1)
next

rem--------- solution on last row ------------------------
d(n) = d(n)/b(n)

rem------------ back substitution ------------------------
for i = n-1 to 1 step -1
  d(i) = (d(i) - a(i)*d(i+1))/b(i)
next

The solution is now in the d(i) array.  If you want to transfer them
to the x(i) array, then another loop will do it.

If your system is block tridiagonal, the you'll need a block
tridiagonal solver.  I've got one if you want it.  

Bob

[original article quoted --djr]
==============================================================================

From: jzhang@cs.engr.uky.edu (Jun Zhang)
Subject: Re: Solve a n x n system with tridiagonal matrix method
Date: 8 Oct 1999 13:19:08 GMT
Newsgroups: sci.math.num-analysis

The LU factorization algorithm of a tridiagonal matrix 
can be found, e.g., on page 45 of P. Wesseling's book
entitled "An Introduction to Multigrid Methods",
Wiley, Chichester, 1992. There is, however, a
printing error in the backsubstitution (4.3.7), the
second formula of the second line should be

u_{k} = y_{k} - \epsilon_{k}u_{k+1},


hope this help.

Jun Zhang
----------

In article <9VlL3.425$_4.692@newsfeeds.bigpond.com>,
robin  <robin_v@bigpond.com> wrote:
[first article above quoted --djr]

--
**********************************************************************
* Jun Zhang                      * E-mail: jzhang@cs.uky.edu         *
* Department of Computer Science * URL:http://www.cs.uky.edu/~jzhang *
* University of Kentucky         * Tel:(606)257-3892                 *