solving triadiagonal (and banded in general) systems of linear equations

[Sergei Steshenko]

Hello,

performing web search I quickly came across 
http://www.gnu.org/software/octave/doc/interpreter/Basic-Matrix-Functions.html 
-> matrix_type , and in the latter I read:

"
'banded'
'banded positive definite'
Banded matrix with the band size of nl below the diagonal and nu above it.  If 
nl and nu are 1, then the matrix is tridiagonal and
treated with specialized code.  In addition the matrix can be marked as
probably a positive definite.  (Sparse matrices only) 
...

Note that the matrix type will be discovered automatically on the first
attempt to solve a linear equation involving A.  Therefore matrix_type is only 
useful to give Octave hints of the matrix type. 
Incorrectly defining the matrix type will result in incorrect results from
solutions of linear equations; it is entirely the responsibility of
the user to correctly identify the matrix type.
".

So, do I understand it correctly, that I simply need to provide matrix to the 
solver, and it will detect automatically that the matrix is banded and choose 
the most optimal algorithm ?


Matrix size is about 200 * 200, so do I need to specify it as a sparse matrix, 
or regular matrix should be OK ? Number of elements is about 4e4, the matrix is 
real, i.e. it should occupy 3.2e5 bytes which is not much by modern standards.

Thanks,
  Sergei.