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Inverse problems are among the most challenging computations in science and engineering because they involve determining the parameters of a system that is only observed indirectly. For example, we might have a spectrum and want to determine the species that produced it as well as their relative proportions, or we may have sonar measurements of a containment tank and want to know whether it has an internal crack. Given a blurred image and a linear model for the blurring, the original image is reconstructed. This linear inverse problem illustrates the impact of ill-conditioning on the choice of algorithms.