Task

Solve   Ax=b   using Gaussian elimination then backwards substitution.

A   being an   n by n   matrix.

Also,   x and b   are   n by 1   vectors.

To improve accuracy, please use partial pivoting and scaling.



See also

   the Wikipedia entry:   Gaussian elimination


 
{require lib_matrix}
 
{M.solve 
 {M.new [[1.00,0.00,0.00,0.00,0.00,0.00],
         [1.00,0.63,0.39,0.25,0.16,0.10],
         [1.00,1.26,1.58,1.98,2.49,3.13],
         [1.00,1.88,3.55,6.70,12.62,23.80],
         [1.00,2.51,6.32,15.88,39.90,100.28],
         [1.00,3.14,9.87,31.01,97.41,306.02]]} 
  [-0.01,0.61,0.91,0.99,0.60,0.02]}
-> 
[-0.01,1.6027903945021094,-1.613203059905548,1.245494121371424,-0.49098971958465304,0.06576069617523143]
 