We show for a specific model problem that the truncation of an unbounded domain by an artificial Dirichlet boundary condition placed far away from the domain of interest is equivalent to a specific absorbing boundary condition at the boundary of the domain of interest. In particular, using Schur complement techniques, we prove that the absorbing boundary condition obtained is a spectral Padé approximation about infinity of the transparent boundary condition. We also study numerically two improvements for this boundary condition-the truncation with an artificial Robin boundary condition placed far away from the domain of interest, and a Padé approximation about different point than infinity. Both of these give new and substantially better results compared to the artificial Dirichlet boundary condition. Seen through the optic of linear algebra, we show that the Schur complement of our model problem written with respect to the eigenbasis can be identified with a truncation of a certain continued fraction. We use the theory of continued fractions to establish an approximation result of this truncation and hence interpreting the Schur complement as the Padé approximation of the optimal boundary operator in the eigenbasis. We then look to further improve the approximation qualities by changing some of the structure of the continued fraction so that the approximation is more accurate around a point of our choice and propose two different ways of achieving this result.