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QR Algorithm

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Fast Compact Algorithms and Software for Spline Smoothing

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

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Abstract

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 using a QR factorization. De Hoog and Hutchinson [1], building on earlier work [2, 3, 4] on general banded least-squares problems, presented a QR algorithm for spline smoothing. In this chapter we will evaluate the condition number of the coefficient matrix, present a faster and more compact QR algorithm, and determine whether this alternative is preferable to solving the normal equations.

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References

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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). QR Algorithm. 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_3

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  • DOI: https://doi.org/10.1007/978-1-4614-5496-0_3

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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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