  We present a construction of a matrix product state (MPS) that approximates
the largest-eigenvalue eigenvector of a transfer matrix T, for the purpose of
rapidly performing the infinite system density matrix renormalization group
(DMRG) method applied to two-dimensional classical lattice models. We use the
fact that the largest-eigenvalue eigenvector of T can be approximated by a
state vector created from the upper or lower half of a finite size cluster.
Decomposition of the obtained state vector into the MPS gives a way of
extending the MPS, at the system size increment process in the infinite system
DMRG algorithm. As a result, we successfully give the physical interpretation
of the product wave function renormalization group (PWFRG) method, and obtain
its appropriate initial condition.
