  Let $\mathcal{O}\subset\mathbb{R}^d$ be a bounded domain of class $C^{1,1}$.
In $L_2(\mathcal{O};\mathbb{C}^n)$, we study a selfadjoint matrix elliptic
second order differential operator $B_{D,\varepsilon}$, $0<\varepsilon\leqslant
1$, with the Dirichlet boundary condition. The principal part of the operator
is given in a factorized form. The operator involves lower order terms with
unbounded coefficients. The coefficients of $B_{D,\varepsilon}$ are periodic
and depend on $\mathbf{x}/\varepsilon$. We study the generalized resolvent
$\left(B_{D,\varepsilon}-\zeta Q_0(\cdot/\varepsilon)\right)^{-1}$, where $Q_0$
is a periodic bounded and positive definite matrix-valued function, and $\zeta$
is a complex-valued parameter. We obtain approximations for the generalized
resolvent in the $L_2(\mathcal{O};\mathbb{C}^n)$-operator norm and in the norm
of operators acting from $L_2(\mathcal{O};\mathbb{C}^n)$ to the Sobolev space
$H^1(\mathcal{O};\mathbb{C}^n)$, with two-parametric error estimates (depending
on $\varepsilon$ and $\zeta$).
