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Fast Compact Algorithms and Software for Spline SmoothingCholesky Algorithm

Fast Compact Algorithms and Software for Spline Smoothing: Cholesky Algorithm [Reinsch [1] provided the first practical algorithm for the continuous case. He solved (1.7)-(1.8) with O(n) floating point operations (flops) using a normalized Cholesky factorization of the coefficient matrix, with a predetermined value for the smoothing parameter. Hutchinson and de Hoog [2] showed that the GCV score could also be evaluated with O(n) flops. However, both execution time and memory use can be reduced substantially by digging deeper into the structure of the problem.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fast Compact Algorithms and Software for Spline SmoothingCholesky Algorithm

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Publisher
Springer New York
Copyright
© The Author(s) 2013
ISBN
978-1-4614-5495-3
Pages
5 –18
DOI
10.1007/978-1-4614-5496-0_2
Publisher site
See Chapter on Publisher Site

Abstract

[Reinsch [1] provided the first practical algorithm for the continuous case. He solved (1.7)-(1.8) with O(n) floating point operations (flops) using a normalized Cholesky factorization of the coefficient matrix, with a predetermined value for the smoothing parameter. Hutchinson and de Hoog [2] showed that the GCV score could also be evaluated with O(n) flops. However, both execution time and memory use can be reduced substantially by digging deeper into the structure of the problem.]

Published: Sep 18, 2012

Keywords: Floating Point Operations; Fminbnd; Vector Splines; Generalized Cross-validation Score; Total Flop Count

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