Fast and stable modification of the Gauss–Newton method for low-rank signal estimation

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Fast and stable modification of the Gauss–Newton method for low-rank signal estimation. / Zvonarev, Nikita ; Golyandina, Nina.

In: Numerical Linear Algebra with Applications, Vol. 29, No. 4, e2428, 08.2022.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{3f16ff9c74234027b172fcffaecd395b,

title = "Fast and stable modification of the Gauss–Newton method for low-rank signal estimation",

abstract = "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.",

keywords = "Gauss–Newton method, Hankel matrix, iterative methods, low-rank approximation, time series, variable projection",

author = "Nikita Zvonarev and Nina Golyandina",

note = "Publisher Copyright: {\textcopyright} 2021 John Wiley & Sons Ltd.",

year = "2022",

month = aug,

doi = "10.1002/nla.2428",

language = "English",

volume = "29",

journal = "Numerical Linear Algebra with Applications",

issn = "1070-5325",

publisher = "Wiley-Blackwell",

number = "4",

}

RIS

TY - JOUR

T1 - Fast and stable modification of the Gauss–Newton method for low-rank signal estimation

AU - Zvonarev, Nikita

AU - Golyandina, Nina

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