  We reconstruct a matrix product state (MPS) in reduced spaces using density
matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each
block contains $N$ physical sites that have a local space of rank $R$. The
simulation in the original spaces of rank $R^N$ is used to construct density
matrices for every block. They are diagonalized and only the eigenvectors
corresponding to significant diagonal elements are used to transform the
original spaces to smaller ones and to reconstruct the MPS in those smaller
spaces accordingly. Simulations in the reduced spaces are used to reliably
extrapolate the result in unreduced spaces. Moreover, to obtain a required
accuracy, the ratio of the reduced space rank over the original decreases
quickly with $N$. The reduced space has a saturated rank to obtain a demanded
accuracy when $N\rightarrow \infty$.
