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Fast Compact Algorithms and Software for Spline Smoothing

Part of the SpringerBriefs in Computer Science Book Series

DOI: 10.1007/978-1-4614-5496-0

ISBN: 978-1-4614-5495-3

Publisher: Springer New York - Springer Journals

Sep 18, 2012

Available

Introduction

Weinert, Howard L.

Pages: 1 –4

[Once upon a time, the most difficult aspect of signal processing was acquiring enough data. Nowadays, one can sample at very high rates and collect huge data sets, but processing the data in a timely manner, without exceeding available memory, is challenging, despite continuing advances in...
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Cholesky Algorithm

Weinert, Howard L.

Pages: 5 –18

[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]...
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QR Algorithm

Weinert, Howard L.

Pages: 19 –28

[The coefficient matrix A (1.9) in the normal equations (1.7) will be ill-conditioned for small λ, causing the number of correct digits in the computed spline to be small. To try to compensate for this problem, one can reformulate spline smoothing as a basic least-squares problem and solve it...
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FFT Algorithm

Weinert, Howard L.

Pages: 29 –35

[For a given λ, the cubic spline smoother is a time-varying linear filter, but it can be approximated by a time-invariant linear filter. It will then be amenable to frequency domain analysis and implementation using the FFT. The FFT algorithm will be compared to the Cholesky algorithm in terms of...
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Discrete Spline Smoothing

Weinert, Howard L.

Pages: 37 –45

[In this chapter we investigate Cholesky and FFT algorithms for discrete cubic spline smoothing, and we compare the performance of the continuous and discrete smoothers. Henderson [1] was the first to use Cholesky factorization for the discrete problem.]

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