On Solving Pentadiagonal Linear Systems via Transformations

Algorithm 3

First symbolic algorithm for solving pentadiagonal linear system.

    To find the solution of PLS (1) using the transformed system (8), we proceed as follows:

INPUT Order of the matrix and the components , , .

OUTPUT The solution vector .

Step  1. Use DETGPENTA algorithm [14] or DETGPENTA algorithm [16] to check the non-singularity of the coefficient matrix

   of the system (1).

Step  2. If , then Exit and Print Message (“No solutions”) end if.

Step  3. Set . If then end if.

Step  4. Set , , and .

Step  5. Set . If then end if.

Step  6. Set , , and .

Step  7. For do

    Compute and simplify:

    ,

    ,

    If then end if.

    ,

    ,

    ,

   End do.

   ,

   . If then end if.

   ,

   ,

   . If then end if.

   ,

   ,

Step  8. Compute the solution vector using , .

   For do

    Compute and simplify:

   End do.

Step  9. Substitute in all expressions of the solution vector .