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Fast Compact Algorithms and Software for Spline SmoothingQR Algorithm

Fast Compact Algorithms and Software for Spline Smoothing: QR Algorithm [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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fast Compact Algorithms and Software for Spline SmoothingQR Algorithm

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/lp/springer-journals/fast-compact-algorithms-and-software-for-spline-smoothing-qr-algorithm-Jp06deO4ri
Publisher
Springer New York
Copyright
© The Author(s) 2013
ISBN
978-1-4614-5495-3
Pages
19 –28
DOI
10.1007/978-1-4614-5496-0_3
Publisher site
See Chapter on Publisher Site

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.]

Published: Sep 18, 2012

Keywords: Condition Number; Coefficient Matrix; Normal Equation; Cholesky Factor; Spline Smoothing

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