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TitleSmoothing splines and rank structured matrices: Revisiting the spline kernel
Author (Name in English or Pinyin)
Andersen, M.S.1; Chen, T.2
Date Issued2020-04-09
Source PublicationSIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
ISSN0895-4798
DOI10.1137/19M1267349
Firstlevel Discipline信息科学与系统科学
Education discipline科技类
Published range国外学术期刊
Volume Issue Pages卷: 41 期: 2 页: 389-412
References
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[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[13] C. H. Reinsch, Smoothing by spline functions, Numer. Math., 10 (1967), pp. 177-183.
[14] C. H. Reinsch, Smoothing by spline functions. II, Numer. Math., 16 (1971), pp. 451-454, https://doi.org/10.1007/bf02169154.
[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.
[16] L. Schumaker, Spline Functions: Basic Theory, Cambridge University Press, Cambridge, UK, 2007.
[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.
[18] R. Vandebril, M. Van Barel, and N. Mastronardi, Matrix Computations and Semiseparable Matrices: Linear Systems, Vol. 1, Johns Hopkins University Press, Baltimore, 2008.
[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.
[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.
Citation statistics
Cited Times:9[WOS]   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Identifierhttps://irepository.cuhk.edu.cn/handle/3EPUXD0A/1341
CollectionSchool of Data Science
Corresponding AuthorAndersen, M.S.
Affiliation
1.Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark
2.School of Science and Engineering, Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen, China
Recommended Citation
GB/T 7714
Andersen, M.S.,Chen, T. Smoothing splines and rank structured matrices: Revisiting the spline kernel[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS,2020.
APA Andersen, M.S., & Chen, T. (2020). Smoothing splines and rank structured matrices: Revisiting the spline kernel. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS.
MLA Andersen, M.S.,et al."Smoothing splines and rank structured matrices: Revisiting the spline kernel".SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS (2020).
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