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Consider an ill-posed problem transformed if necessary so that the errors in the data are independent identically normally distributed with mean zero and variance 1. We survey regularization and parameter selection from a linear algebra and statistics viewpoint and compare the statistical distributions of regularized estimates of the solution and the residual. We discuss methods for choosing a regularization parameter in order to assure that the residual for the model is statisticallydoi:10.1088/0266-5611/24/3/034005 fatcat:lk7lboym5nfbjp2bgir3btdici