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Abstract.Round off error analysis for the classical Gram-Schmidt orthogonalization method with re-orthogonalization is presented. The effect of the round-off error on the orthogonality of the derived vectors and also on the solution of the linear least squares problems when solved by the Gram-Schmidt algorithm are given. Numerical results compared favorably with the results of other methods. The classical case when no re-or~hogonalization takes place is also discussed.

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Abstract.A simplex algorithm for the Chebyshev solution of overdetermined systems of linear equations is described. In this algorithm, an initial basic feasible solution is available with no artificial variables needed. Also minimum storage is required and no conditions are imposed on the coefficient matrix. The algorithm is a simple and fast one. Numerical results are given.