Summary
In this paper, overdetermined systems ofm linear equations inn unknowns are considered. Withℝ m equipped with a smooth strictly convex norm, ‖·‖, an iterative algorithm for finding the best approximate solution of the linear system which minimizes the ‖·‖-error is given. The convergence of the algorithm is established and numerical results are presented for the case when ‖·‖ is anl p norm, 1<p<∞.
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References
Sreedharan, V.P.: Least squares algorithms for finding solutions of overdetermined systems of linear equations which minimize error in a smooth strictly convex norm. J. Approximation Theory8, 46–61 (1973)
Barrodale, I., Young, A.: Algorithms for bestL 1 andL ∞ linear approximations on a discrete set. Numer. Math.8, 295–306 (1966)
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Portions of this paper are taken from the author's Ph.D. thesis at Michigan State University
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Owens, R.W. An algorithm for best approximate solutions ofAx=b with a smooth strictly convex norm. Numer. Math. 29, 83–91 (1977). https://doi.org/10.1007/BF01389315
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DOI: https://doi.org/10.1007/BF01389315