Statistical Estimates for the Conditioning of Linear Least Squares Problems

In this paper we are interested in computing linear least squares (LLS) condition numbers to measure the numerical sensitivity of an LLS solution to perturbations in data. We propose a statistical estimate for the normwise condition number of an LLS solution where perturbations on data are mesured using the Frobenius norm for matrices and the Euclidean norm for vectors. We also explain how condition numbers for the components of an LLS solution can be computed. We present numerical experiments that compare the statistical condition estimates with their corresponding exact values.

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