CGLS-GCV: a hybrid algorithm for low-rank-deficient problems Original Research Article

Given View the MathML source, where rank(A)⪡min(m,n), and View the MathML source, we investigate the following problems: (a) the construction of approximate minimum norm solutions of the least squares problem min‖Ax−b‖, and (b) the computation of approximations of the column (row) subspace of A. We propose an algorithm for solving these problems based on conjugate gradient iterations followed by regularization in the generated Krylov subspace. Regularization is introduced for estimating rank(A) and implemented using the generalized cross-validation technique. We report the outcome of numerical experiments, showing that the new algorithm yields results with accuracy comparable to that of the SVD, but at a lower computational cost.