Summary
The convergence properties of an algorithm for discreteL p approximation (1≦p<2) that has been considered by several authors are studied. In particular, it is shown that for 1<p<2 the method converges (with a suitably close starting value) to the best approximation at a geometric rate with asymptotic convergence constant 2-p. A similar result holds forp=1 if the best approximation is unique. However, in this case the convergence constant depends on the function to be approximated.
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Wolfe, J.M. On the convergence of an algorithm for discreteL p approximation. Numer. Math. 32, 439–459 (1979). https://doi.org/10.1007/BF01401047
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DOI: https://doi.org/10.1007/BF01401047