## Algorithms for overdetermined systems of equations |

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A/-invariant approximation assume backward error Bjorck column permutations column pivoting computed condition number constrained and weighted constrained least squares constrained linear least continuation method convergence rate define duality curves error analysis estimation Explicit Implicit following theorem Gauss-Newton method global convergence GNCS gNR method Householder reflections ill conditioned infinite weights Info Inst Jacobian Jkpk least squares problem Lemma line search linear least squares linearly independent lp norm M-invariant reflections M. E. Gulliksson MARTEN gulliksson merit weights modified QR decomposition Newton method nonlinear least squares nonsingular norm number of iterations orthogonal overdetermined system p-curve p-problem parameters per-Ake wedin permutation matrix Proc proof QMQT rank deficient second order information second order method SIAM solving 1.1 Sweden system equations system matrix system of equations Technical Report UMINF test example unique Univ unweighted upper triangular vector weighted and constrained weighted least squares weighted linear least weighted QR decomposition zero residuals