Computing a Jacobi iteration with the WL?

Questions
,
1

Hey!

I’m trying to implement the Jacobi iteration in Mathematica, but it does not work… I’m a beginner in Mathematica, can anybody help?

Here’s my code:

jac[A_, b_, xstart_] := Module[{n, k, i, j, xneu, xalt},
   n = Length[b];
   xalt = xstart;
   While[k < 10000,
     xneu = b;
     For[i = 1, i <= n, i++,
        For[j = 1, j <= n, j++,
            If[i != j,
             xneu[[i]] = xneu[[i]] - A[[i, j]]*xalt[j];
             ]
            ]
           xneu[[i]] = xneu[[i]]/A[[i, i]];
        ]
       xalt = xneu;
     k++;
     ]
    Return[xalt];
   ];
2

What exactly doesn’t work? Do you get an error? What input did you use?

3

My input is:
A = {{10, 14, 11}, {13, -66, 14}, {11, -13, 12}}; b = {1, 1, 1}; xstart = {0, 0, 0}; Print[jac[A, b, xstart]];

Output is nothing. What am I doing wrong?

Edit: Outpus is jac[{{10,14,11},{13,-66,14},{11,-13,12}},{1,1,1},{0,0,0}].

4

Here are two items that need fixing (but there are more things to fix):

  1. k needs to be initialized.
  2. There is an instance of xalt[j] that should be xalt[[j]].
5

Does this do what you want? (I’ve reduced the number of iterations to 10 to minimize the output.)

jac[A_, b_, xstart_] := Module[{n, k, i, j, xneu, xalt},
   n = Length[b];
   xalt = xstart;
   k = 0;
   While[k < 10,
    xneu = b;
    For[i = 1, i <= n, i++,
     For[j = 1, j <= n, j++, 
      If[i != j, xneu[[i]] = xneu[[i]] - A[[i, j]]*xalt[[j]]]];
      xneu[[i]] = xneu[[i]]/A[[i, i]]]; 
    xalt = xneu;
    k++]; 
   xalt];
A = {{10, 14, 11}, {13, -66, 14}, {11, -13, 12}};
b = {1, 1, 1};
xstart = {0, 0, 0};
jac[A, b, xstart]
(* {1382598113217283/36067178188800000, 
  379022657204357/22132132070400000, 
  -(4712310469911859/486906905548800000)} *)