Abstract
An algorithm for approximating a non negative solution of inconsistent systems of linear equations is presented. We define a best approximate solution of a system Ax = b x≥0 to be the vector x≥0 which minimizes the norm of the residual r(x) = b − Ax, for a smooth and strictly convex norm. The algorithm is shown to be feasible and globally convergent. The special case of the ℓ p norm is included. In particular, the method converges for 1 < p < 2. A generalization of this algorithm is also given. Numerical results are included.
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