I must add to may program GS algorithm for soloving linear equation (i already hav gauss elimination and LU algorithm).
I make function (but it not works, please corect me :( :( :


where:
n -dimensin of main matrix
tab - main matrix
itmax - max number of iteration
prec- precisin
start - initial for xold and x vector


void GS_solve(type **tab,type *b, type *x, const int &n,double prec, int itmax, type start){
double suma,m;
double error=1.;
type *xold=new type[n];
for(int i=0;i<n;++i){
xold[i]=start;
x[i]=start;
}
for(int it=1;it<itmax;++it){
if(error>prec){
for(int i=0;i<n;++i){
suma=0;
for(int j=0;j<i;++j){
suma+=tab[i][j]*x[j];
}
for(int j=i+1;j<n;++j){
suma+=tab[i][j]*xold[j];
}
x[i]=(b[i]-suma)/tab[i][i];
}
}else break;
error=0.;
for(int k=0;k<n;++k){
m=fabs(x[k]-xold[k]);
if(error<m) error=m;
xold[k]=x[k];
}
}
delete [] xo;
}


PS.Sorry for my bad englisch

Here's what I did for the Gauss Seidel. You can get away with only using one array for your solution Vector (X) and therefore you only have one loop, which makes your code look cleaner.

For the system Ax = b


double * x = new double [rows];
double sum = 0;

for (int l = 0; l < rows; l++)
x[l] = 0;

while(iterations--)
{
for(int i = 1; i <= rows; i++)
{
sum = b[i-1];
for(int j = 1; j <= rows; j++)
{
if( i != j )
{
sum = sum - (el[i][j] * x[j-1]);
}
}
x[i-1] = sum/el[i][i];
}
}


Background on my code: el is my two-dimensional array (Matrix A) and it is 1 based, to make my matrix class nice (or at least I think it is). However, the X and b vectors are zero based, which is why I have the j-1 and i-1 for those. Also, I know a lot of people will have the while loop condition statement check between previous values. I just gave it a set number of iterations to go, but it wouldn't be hard to change that. This also doesn't have relaxations either. That wouldn't be hard to add either. I was mainly trying to get the bare bones for the algorithm while keeping everything really clean. Hope this helps!