function Y = sylv_triangular(UA, LB, E)
% solve the equation UA*Y - Y*LB = E,
% where UA is upper tr., LB is lower tr.

[m, n] = size(E);

Y = zeros(m, n);
for j = n:-1:1
    for i = m:-1:1
        num = E(i,j) - UA(i,i+1:end)*Y(i+1:end,j) + Y(i,j+1:end)*LB(j+1:end,j);
        Y(i,j) = num / (UA(i,i)-LB(j,j));
    end
end