Abstract
Abstract. In this paper, we prove that Newton's method for convex best interpolation is locally quadratically convergent, giving an answer to a question of Irvine, Marin, and Smith [7] and strengthening a result of Andersson and Elfving [1] and our previous work [5]. A damped Newton-type method is presented which has global quadratic convergence. Analogous results are obtained for the convex smoothing problem. Numerical examples are presented.
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Dontchev, Qi & Qi Quadratic Convergence of Newton's Method for Convex Interpolation and Smoothing . Constr. Approx. 19, 123–143 (2003). https://doi.org/10.1007/s00365-002-0513-2
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DOI: https://doi.org/10.1007/s00365-002-0513-2