March  2004, 3(1): 133-148. doi: 10.3934/cpaa.2004.3.133

A Newton-type method for computing best segment approximations

1. 

Celera Genomics, South San Francisco, CA 94080, United States

Received  January 2003 Revised  September 2003 Published  January 2004

This paper presents a new method for computing best segment approximations. It is based on Newton iteration, but modified to obtain global convergence. The method is described in detail and a thorough convergence analysis is given. Polynomials are used as approximating functions. Not that the basic method will produce approximations that are not smooth and coninuity is not guaranteed. Howwever, we will describe applications to produce smooth spline approximation with free knots.
Citation: Hans J. Wolters. A Newton-type method for computing best segment approximations. Communications on Pure & Applied Analysis, 2004, 3 (1) : 133-148. doi: 10.3934/cpaa.2004.3.133
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