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Mathematics Calculus Wolfram Language Numerical Computation

Computing a Jacobi iteration with the WL?

gabse15 l

Posted 9 years ago

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]; ];

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];
   ];

POSTED BY: gabse15 l

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Jim Baldwin

Jim Baldwin, Retired

Posted 9 years ago

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)} *)

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)} *)

POSTED BY: Jim Baldwin

Jim Baldwin

Jim Baldwin, Retired

Posted 9 years ago

Here are two items that need fixing (but there are more things to fix): `k` needs to be initialized. There is an instance of `xalt[j]` that should be `xalt[[j]]`.

POSTED BY: Jim Baldwin

gabse15 l

Posted 9 years ago

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}]`.

POSTED BY: gabse15 l

Jim Baldwin

Jim Baldwin, Retired

Posted 9 years ago

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

POSTED BY: Jim Baldwin

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