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.
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References
Reinsch CH (1967) Smoothing by spline functions. Numer Math 10:177–183
Hutchinson MF, de Hoog FR (1985) Smoothing noisy data with spline functions. Numer Math 47:99–106
Bauer FL (1955) Ein direktes iterationsverfahren zur Hurwitz-zerlegung eines polynoms. Arch Elektr Ubertragung 9:285–290
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Weinert, H.L. (2013). Cholesky 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_2
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DOI: https://doi.org/10.1007/978-1-4614-5496-0_2
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