Quadratic Convergence of Newton's Method for Convex Interpolation and Smoothing |
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| Authors: | Dontchev Qi Qi |
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| Affiliation: | (1) Mathematical Reviews Ann Arbor, MI 48107 USA ald@ams.org, US;(2) School of Mathematics The University of New South Wales Sydney New South Wales 2052 Australia hdqi@maths.unsw.edu.au, AU;(3) Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong maqilq@polyu.edu.hk, HK |
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| 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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| Keywords: | . Convex best interpolation Convex smoothing Splines Newton's method Quadratic convergence. AMS Classification. 41A29 65D15 49J52 90C25. |
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