Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Fast and stable modification of the Gauss–Newton method for low-rank signal estimation. / Zvonarev, Nikita; Golyandina, Nina.
в: Numerical Linear Algebra with Applications, Том 29, № 4, e2428, 08.2022.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Fast and stable modification of the Gauss–Newton method for low-rank signal estimation
AU - Zvonarev, Nikita
AU - Golyandina, Nina
N1 - Publisher Copyright: © 2021 John Wiley & Sons Ltd.
PY - 2022/8
Y1 - 2022/8
N2 - The weighted nonlinear least-squares problem for low-rank signal estimation is considered. The problem of constructing a numerical solution that is stable and fast for long time series is addressed. A modified weighted Gauss–Newton method, which can be implemented through the direct variable projection onto a space of low-rank signals, is proposed. For a weight matrix that provides the maximum likelihood estimator of the signal in the presence of autoregressive noise of order p the computational cost of iterations is (Formula presented.) as N tends to infinity, where N is the time-series length, r is the rank of the approximating time series. Moreover, the proposed method can be applied to data with missing values, without increasing the computational cost. The method is compared with state-of-the-art methods based on the variable projection approach in terms of floating-point numerical stability and computational cost.
AB - The weighted nonlinear least-squares problem for low-rank signal estimation is considered. The problem of constructing a numerical solution that is stable and fast for long time series is addressed. A modified weighted Gauss–Newton method, which can be implemented through the direct variable projection onto a space of low-rank signals, is proposed. For a weight matrix that provides the maximum likelihood estimator of the signal in the presence of autoregressive noise of order p the computational cost of iterations is (Formula presented.) as N tends to infinity, where N is the time-series length, r is the rank of the approximating time series. Moreover, the proposed method can be applied to data with missing values, without increasing the computational cost. The method is compared with state-of-the-art methods based on the variable projection approach in terms of floating-point numerical stability and computational cost.
KW - Gauss–Newton method
KW - Hankel matrix
KW - iterative methods
KW - low-rank approximation
KW - time series
KW - variable projection
UR - http://www.scopus.com/inward/record.url?scp=85121453928&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/c2dd364b-939b-3281-9b4a-d25ac057f66c/
U2 - 10.1002/nla.2428
DO - 10.1002/nla.2428
M3 - Article
AN - SCOPUS:85121453928
VL - 29
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
SN - 1070-5325
IS - 4
M1 - e2428
ER -
ID: 93205595