zbMATH — the first resource for mathematics

Smoothing splines and rank structured matrices: revisiting the spline kernel. (English) Zbl 1440.65038
65F05 Direct numerical methods for linear systems and matrix inversion
65D07 Numerical computation using splines
65D10 Numerical smoothing, curve fitting
60G15 Gaussian processes
65C20 Probabilistic models, generic numerical methods in probability and statistics
Full Text: DOI
[1] F. P. Carli, T. Chen, and L. Ljung, Maximum entropy kernels for system identification, IEEE Trans. Automat. Control, 62 (2017), pp. 1471-1477, https://doi.org/10.1109/tac.2016.2582642. · Zbl 1366.93669
[2] T. Chen, T. Ardeshiri, F. P. Carli, A. Chiuso, L. Ljung, and G. Pillonetto, Maximum entropy properties of discrete-time first-order stable spline kernel, Automatica, 66 (2016), pp. 34-38, https://doi.org/10.1016/j.automatica.2015.12.009. · Zbl 1335.93131
[3] A. M. Erisman and W. F. Tinney, On computing certain elements of the inverse of a sparse matrix, Commun. ACM, 18 (1975), pp. 177-179, https://doi.org/10.1145/360680.360704. · Zbl 0296.65012
[4] D. Foreman-Mackey, E. Agol, S. Ambikasaran, and R. Angus, Fast and scalable Gaussian process modeling with applications to astronomical time series, Astronom. J., 154 (2017), p. 220, https://doi.org/10.3847/1538-3881/aa9332.
[5] Y. Fujimoto and T. Chen, On the Coordinate Change to the First-Order Spline Kernel for Regularized Impulse Response Eestimation, https://arxiv.org/abs/arXiv:1901.10835, 2019.
[6] G. H. Golub and C. F. V. Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 2013. · Zbl 1268.65037
[7] M. F. Hutchinson and F. R. de Hoog, Smoothing noisy data with spline functions, Numer. Math., 47 (1985), pp. 99-106, https://doi.org/10.1007/bf01389878. · Zbl 0578.65009
[8] J. Keiner and B. J. Waterhouse, Fast principal components analysis method for finance problems with unequal time steps, in Monte Carlo and Quasi-Monte Carlo Methods 2008, Springer, Berlin, 2009, pp. 455-465, https://doi.org/10.1007/978-3-642-04107-5_29. · Zbl 1182.91200
[9] G. Kimeldorf and G. Wahba, Some results on Tchebycheffian spline functions, J. Math. Anal. Appl., 33 (1971), pp. 82-95, https://doi.org/10.1016/0022-247x(71)90184-3. · Zbl 0201.39702
[10] R. Kohn and C. F. Ansley, A new algorithm for spline smoothing based on smoothing a stochastic process, SIAM J. Sci. Stat. Comput., 8 (1987), pp. 33-48, https://doi.org/10.1137/0908004. · Zbl 0627.65010
[11] J. H. Manton and P.-O. Amblard, A primer on reproducing kernel Hilbert spaces, Found. Trends Signal Process., 8 (2015), pp. 1-126, https://doi.org/10.1561/2000000050. · Zbl 1377.46015
[12] G. Pillonetto and G. De Nicolao, A new kernel-based approach for linear system identification, Automatica, 46 (2010), p. 81-93, https://doi.org/10.1016/j.automatica.2009.10.031. · Zbl 1214.93116
[13] C. H. Reinsch, Smoothing by spline functions, Numer. Math., 10 (1967), pp. 177-183. · Zbl 0161.36203
[14] C. H. Reinsch, Smoothing by spline functions. II, Numer. Math., 16 (1971), pp. 451-454, https://doi.org/10.1007/bf02169154. · Zbl 1248.65020
[15] I. J. Schoenberg, Spline functions and the problem of graduation, Proc. Natl. Acad. Sci., 52 (1964), pp. 947-950, https://doi.org/10.1073/pnas.52.4.947. · Zbl 0147.32102
[16] L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, UK, 2007. · Zbl 1123.41008
[17] R. Vandebril, M. Van Barel, and N. Mastronardi, Matrix Computations and Semiseparable Matrices: Eigenvalue and Singular Value Methods, Vol. 2, Johns Hopkins University Press, Baltimore, 2008. · Zbl 1175.65045
[18] R. Vandebril, M. Van Barel, and N. Mastronardi, Matrix Computations and Semiseparable Matrices: Linear Systems, Vol. 1, Johns Hopkins University Press, Baltimore, 2008. · Zbl 1141.65019
[19] G. Wahba, Improper priors, spline smoothing and the problem of guarding against model errors in regression, J. Roy. Statist. Soc. Ser. B, 40 (1978), pp. 364-372, http://www.jstor.org/stable/2984701. · Zbl 0407.62048
[20] G. Wahba, Spline Models for Observational Data, CBMS-NSF Regional Conf. Ser. in Appl. Math. 59, SIAM, Philadelphia, 1990, https://doi.org/10.1137/1.9781611970128. · Zbl 0813.62001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.