Forward Elimination: for k=1…n-1 for i=k+1…n pivot = A(i,k)/A(k,k) for j=k…n A(i,j) = A(i,j) - pivot * A(k,j) end B(i) = B(i) - pivot * B(k) end end Back Substitution: X(n) = B(n)/A(n,n); for i=n-1…1 step-1 sum = 0 for j=i+1…n sum = sum + A(I,j)*X(j) end X(i) = (B(i)-sum) / A(i,i) end Pivoting: i_pivot = k big = |a(k,k)| for ii = k+1…n dumy = |a(ii,k)| if ( dumy>big ) big = dumy i_pivot = ii end if end if (i_pivot ~= k) for jj = k…n dummy = A(pivot,jj) A(i_pivot,jj)=A(k,jj) A(k,jj)=dummy; end dummy = C(i_pivot) C(i_pivot) = C(k) C(k) = dummy End if

Forward Elimination:

for k=1…n-1

      for i=k+1…n

           pivot = A(i,k)/A(k,k)

           for j=k…n  

                A(i,j) = A(i,j) - pivot * A(k,j)

           end

           B(i) = B(i) - pivot * B(k)

      end

end

Back Substitution:

X(n) = B(n)/A(n,n);

for i=n-1…1  step-1

      sum = 0

      for j=i+1…n

           sum = sum + A(I,j)*X(j)

      end

      X(i) = (B(i)-sum) / A(i,i)

end

Pivoting:

i_pivot = k

big = |a(k,k)|

for ii = k+1…n

      dumy = |a(ii,k)|

      if ( dumy>big )

          big = dumy

          i_pivot = ii

      end if

end

if (i_pivot ~= k)

    for jj = k…n

        dummy = A(pivot,jj)

        A(i_pivot,jj)=A(k,jj)

        A(k,jj)=dummy;

    end

    dummy = C(i_pivot)

    C(i_pivot) = C(k)

    C(k) = dummy

End if