  A novel matrix approximation problem is considered herein: observations based
on a few fully sampled columns and quasi-polynomial structural side information
are exploited. The framework is motivated by quantum chemistry problems wherein
full matrix computation is expensive, and partial computations only lead to
column information. The proposed algorithm successfully estimates the column
and row-space of a true matrix given a priori structural knowledge of the true
matrix. A theoretical spectral error bound is provided, which captures the
possible inaccuracies of the side information. The error bound proves it scales
in its signal-to-noise (SNR) ratio. The proposed algorithm is validated via
simulations which enable the characterization of the amount of information
provided by the quasi-polynomial side information.
