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Fast Compact Algorithms and Software for Spline Smoothing pp 1–4Cite as

Introduction

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Abstract

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 computer technology. Meeting this challenge requires the full exploitation of mathematical structure to develop an algorithm that can be implemented efficiently in software.

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References

  1. Bohlmann G (1899) Ein ausgleichungsproblem. Nachr Ges Wiss Gott Math-Phys Kl:260–271

    Google Scholar 

  2. Whittaker ET (1923) On a new method of graduation. Proc Edinb Math Soc 41:63–75

    Google Scholar 

  3. Henderson R (1925) Further remarks on graduation. Trans Actuar Soc Am 26:52–57

    Google Scholar 

  4. Spoerl CA (1937) The Whittaker-Henderson graduation formula A. Trans Actuar Soc Am 38:403-462

    Google Scholar 

  5. Hodrick RJ, Prescott EC (1997) Postwar US business cycles: an empirical investigation. J Money Credit Bank 29:1–16

    Article  Google Scholar 

  6. Schoenberg IJ (1964) Spline functions and the problem of graduation. Proc Natl Acad Sci 52:947–950

    Article  MathSciNet  MATH  Google Scholar 

  7. Reinsch CH (1967) Smoothing by spline functions. Numer Math 10:177–183

    Article  MathSciNet  MATH  Google Scholar 

  8. Cook ER, Peters K (1981) The smoothing spline: a new approach to standardizing forest interior tree-ring width series for dendroclimatic studies. Tree-Ring Bull 41:45–53

    Google Scholar 

  9. Carew JD, Wahba G, Xie X, Nordheim EV, Meyerand ME (2003) Optimal spline smoothing of fMRI time series by generalized cross-validation. NeuroImage 18:950–961

    Article  Google Scholar 

  10. Kuligowski J, Carrion D, Quintas G, Garrigues S, de la Guardia M (2010) Cubic smoothing splines background correction in on-line liquid chromatography-Fourier transform infrared spectrometry. J Chromatogr. A 1217:6733–6741

    Article  Google Scholar 

  11. Wahba G (1990) Spline models for observational data. SIAM, Philadelphia

    Book  MATH  Google Scholar 

  12. Green PJ, Silverman BW (1994) Nonparametric regression and generalized linear models. Chapman and Hall, London

    MATH  Google Scholar 

  13. Weinert HL (2007) Efficient computation for Whittaker-Henderson smoothing. Comput Stat Data Anal 52:959–974

    Article  MathSciNet  MATH  Google Scholar 

  14. Weinert HL (2009) A fast compact algorithm for cubic spline smoothing. Comput Stat Data Anal 53:932–940

    Article  MathSciNet  MATH  Google Scholar 

  15. Lee TCM (2003) Smoothing parameter selection for smoothing splines: a simulation study. Comput Stat Data Anal 42:139–148

    Article  MATH  Google Scholar 

  16. Brent RP (1973) Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

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Authors and Affiliations

  1. Johns Hopkins University, Baltimore, MD, USA

    Howard L. Weinert

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  1. Howard L. Weinert
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Weinert, H.L. (2013). Introduction. In: Fast Compact Algorithms and Software for Spline Smoothing. SpringerBriefs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5496-0_1

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  • DOI: https://doi.org/10.1007/978-1-4614-5496-0_1

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-5495-3

  • Online ISBN: 978-1-4614-5496-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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