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On Applying Optimal Design of Experiments when Functional Observations Occur Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Analysis and Design in the Problem of Vector Deconvolution

Authors : Anatoly Zhigljavsky, Nina Golyandina, Jonathan Gillard

Published in: mODa 11 - Advances in Model-Oriented Design and Analysis

Publisher: Springer International Publishing

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Abstract

We formulate the problem of deconvolution of a given vector as an optimal design problem and suggest numerical algorithms for solving this problem. We then discuss an important application of the proposed methods for problems of time series analysis and signal processing and also to the low-rank approximation of structured matrices.

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previous chapter Functional Data Analysis in Designed Experiments
Literature
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Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge/New York (2004)CrossRefMATH
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Gillard, J., Zhigljavsky, A.: Optimization challenges in the structured low rank approximation problem. J. Glob. Optim. 57, 733–751 (2013)CrossRefMATHMathSciNet
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Gillard, J., Zhigljavsky, A.: Application of structured low-rank approximation methods for imputing missing values in time series. Stat. Interface 8, 321–330 (2015)CrossRefMathSciNet
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Gillard, J., Zhigljavsky, A.: Stochastic algorithms for solving structured low-rank matrix approximation problems. Commun. Nonlinear Sci. Numer. Simul. 21, 70–88 (2015)CrossRefMATHMathSciNet
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Golyandina, N., Korobeynikov, A.: Basic singular spectrum analysis and forecasting. R. Comput. Stat. Data Anal. 71, 934–954 (2014)CrossRefMathSciNet
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Golyandina, N., Nekrutkin, V., Zhigljavsky, A.: Analysis of Time Series Structure: SSA and Related Techniques. CRC Press, Boca Raton (2001)CrossRefMATH
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Golyandina, N., Shlemov, A.: Variations of singular spectrum analysis for separability improvement: non-orthogonal decompositions of time series. Stat. Interface 8, 277–294 (2015)CrossRefMathSciNet
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Golyandina, N., Zhigljavsky, A.: Singular Spectrum Analysis for Time Series. Springer, New York (2013)CrossRefMATH
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Zhigljavsky, A.A.: Theory of Global Random Search. Kluwer Academic Press, Dordrecht (1991)CrossRef
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Metadata
Title
Analysis and Design in the Problem of Vector Deconvolution
Authors
Anatoly Zhigljavsky
Nina Golyandina
Jonathan Gillard
Copyright Year
2016
Book
mODa 11 - Advances in Model-Oriented Design and Analysis

Print ISBN: 978-3-319-31264-4

Electronic ISBN: 978-3-319-31266-8

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-31266-8_28

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