forward_elim()

function x = forward_elim(L, b)
   n = length(b);
   x = zeros(n, 1);
   x(1) = b(1)/L(1, 1);
   for i = 2:n
     sum = 0;
     for j = 1:i-1
       sum = sum + L(i, j) * x(j);
     endfor
     x(i) = (b(i)-sum)/L(i, i);
   endfor
endfunction