Most reconstruction algorithms for transmission tomography can be subdivided in two classes: variants of filtered backprojection (FBP) and iterative algebraic methods. FBP is very fast and yields accurate results when a large number of projections are available, with high signal-to-noise ratio and a full angular range. Algebraic methods require much more computation time, yet they are more flexible in dealing with limited data problems and noise. In this paper, we propose an algorithm that combines the best of these two approaches: for a given linear algebraic method, a filter is computed that can be used within the FBP algorithm. The FBP reconstructions that result from using this filter strongly resemble the algebraic reconstructions and have many of their favorable properties, while the required reconstruction time is similar to standard-FBP. Based on a series of experiments, for both simulation data and experimental data, we demonstrate the merits of the proposed algorithm.