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Tridiagonal matrix with fringes

  1. Apr 3, 2014 #1
    Hello everyone!

    I am trying to solve a large system of linear equations. The form of the matrix is A = T + F. T is basically a tridiagonal matrix and F has two "lines" of numbers running parallel to the diagonal but at some distance. Basically like this one, but not symmetric, nor is it diagonally dominant.

    Is there any efficient algorithm to solve this kind of matrix?

    Is there any way to turn the matrix into a diagonally dominant one, so that a straight forward iterative method could be used?

    Could one make a custom iterative method, that does not require diagonal dominance? Would [itex]\overline{x}_{i+1} = T^{-1}(\overline{b}-F \overline{x}_{i}) [/itex] work?
  2. jcsd
  3. Apr 3, 2014 #2


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    There are routines designed to solve sparse, banded matrices.



    I would suggest you look at the routines SPARSE 1.3 and SPARSE-BLAS on netlib as these are collections of routines designed to deal with sparse matrices:


    There is also a proprietary set of routines called SPARSPAK which is available from the U of Waterloo in Canada.

    In general, these routines will optimize storing the sparse matrix (since most of the elements are zero, a considerable savings in memory space can be obtained) and also apply pre-conditioning to improve the accuracy of the solution.
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