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Manuscript Title: Application of the generalized backward substitution method to solve a class of linear systems.
Authors: R. Calinon, J. Ligou
Program title: APICS
Catalogue identifier: ACZJ_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)317
Programming language: Fortran.
Computer: C.D.C. 7326.
Operating system: N.O.S. B.E.
RAM: 4K words
Word size: 60
Peripherals: disc.
Keywords: General purpose, Matrix, Backward substitution, Band matrices, Linear systems.
Classification: 4.8.

Nature of problem:
General purpose subprogram solving linear systems corresponding to tridiagonal matrices in which the elements are replaced by submatrices. As an example, one can mention the discretized form (in time and space) of very general parabolic equations. A stable numerical scheme leads to such a system of linear equations.

Solution method:
Generalization to matrices of the backward substitution method.

Restrictions:
All the submatrices have the same dimensions.

Unusual features:
The same problem might be solved by some classical methods, but the proposed method allows us to leave out all the zeros of the matrix and to save memory and CPU time.

Running time:
The running time depends on two parameters: n: dimension of submatrices I: number of submatrices along the diagonal For example:
                                                            
                                                                         
 ---------------------------------------------------------               
  n               I                    Time of CPU                       
 ---------------------------------------------------------               
  10               5                   0.940                             
   5              10                   0.438                             
  10              10                   2.079                             
   5              20                   0.964                             
  20               5                   5.468                             
 ---------------------------------------------------------