Overview of the main program (either language)

Your sample program (diffusion) will accomplish the following tasks:
1. Set up a matrix A (which is N by N, N chosen at run time) as well as the corresponding right hand side b for the system to be solved, A x = b, for a computed value x_computed. These have been chosen to describe the heat diffusion structure.
2. Call the routine sgeco to perform Gaussian Elimination with partial pivoting. The work is

   
   2N^3 - 3N^2 + N                      N^3 - N
   ---------------  Adds/Subtracts      -------  Multiplies/Divides
         6                                  3 
   
   

   For "large enough" N, both of these terms is dominated by its high order term which is N^3/3 for both counts.
3. Call the routine sgesl to solve the system A x = b for the computed answer, x_computed. The work is

   N^2 - N  Adds/Subtracts       N^2 Multiplies/Divides
   

   For "large enough" N, both of these terms are dominated by N^2.
4. Output statistics of the run:
   • Size of linear system, N
   • Time to assemble the matrix A and right hand side b
   • Time to compute the GE factorization
   • Time to compute the solution, b, for A x = b
   • Estimated condition number of the matrix A, K(A)