A Newton-type method for computing best segment approximations

Hans J. Wolters

doi:10.3934/cpaa.2004.3.133

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2004, Volume 3, Issue 1: 133-149 . Doi: 10.3934/cpaa.2004.3.133

This issue Previous Article Existence and regularity results for the primitive equations in two space dimensions Next Article Asymptotic behavior of the $L^1$ norm of solutions to nonlinear parabolic equations

A Newton-type method for computing best segment approximations

Hans J. Wolters^1,

1.
Celera Genomics, South San Francisco, CA 94080

Received: December 31, 2002

Revised: August 31, 2003

Published: February 2004

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Abstract

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.

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Mathematics Subject Classification: 41A15, 41A50.

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