This is a very simple Pascal program I wrote in mid 1990s, which solves a sparse NxN linear system using the Succesive Overrelaxation Method (SOR), which in turn is based on Gauss Seidel Method.
Both methods are iterative.

N is initially set at maximum …64.
You need the W factor for the SOR to complete successful. The theory assures us that it must be W=1.062.

```PROGRAM SOR; uses crt; VAR A: array [1..64,1..64] of real; B,X,XT: array [1..64] of real; I,J,K,L,M,N,ROW1,COL1,REP,MAX : integer; SUM,W: real; LABEL ALPHA,BETA;   begin   clrscr;   SUM:=0;   WRITELN ('PLEASE ENTER N:'); READLN ( N);   CLRSCR;   WRITELN ('PLEASE, ENTER MATRIX A NxN, LINE BY LINE:'); FOR I:=1 TO N DO FOR J:=1 TO N DO BEGIN READ (A[I,J]); END;   CLRSCR;   WRITELN ('PLEASE, ENTER MATRIX B Nx1 :'); FOR I:=1 TO N DO BEGIN READ (B[I]); END;   CLRSCR;   WRITELN ('PLEASE, ENTER YOUR VECTOR X:'); FOR I:=1 TO N DO BEGIN READ (X[I]); END;   CLRSCR;   WRITELN ('PLEASE ENTER NUMBER OF REPEATS:'); READ (MAX);   CLRSCR;   WRITELN ('PLEASE ENTER W:'); READ ( W);   { MAIN GAUSS SEIDEL ALGORITHM }   FOR REP:=1 TO MAX DO BEGIN FOR I:=1 TO N DO BEGIN SUM:=0; IF I=1 THEN GOTO ALPHA; FOR J:=1 TO I-1 DO BEGIN SUM:=SUM+A[I,J]*X[J]; END; ALPHA: IF I=N THEN GOTO BETA; FOR K:=I+1 TO N DO BEGIN SUM:=SUM+A[I,K]*X[K]; END; BETA:X[I]:=((W/A[I,I])*(B[I]-SUM))-(W-1)*X[I]; END; END;   CLRSCR;   WRITELN ('X='); FOR I:=1 TO N DO BEGIN WRITELN (X[I]); END;   WRITELN ('any key to continue!'); READLN;READLN;   END.```
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