Standard

Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. / Zvonarev, Nikita; Golyandina, Nina.

In: Algorithms, Vol. 15, No. 12, 460, 05.12.2022.

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

Harvard

Zvonarev, N & Golyandina, N 2022, 'Mixed Alternating Projections with Application to Hankel Low-Rank Approximation', Algorithms, vol. 15, no. 12, 460. https://doi.org/10.3390/a15120460

APA

Zvonarev, N., & Golyandina, N. (2022). Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. Algorithms, 15(12), [460]. https://doi.org/10.3390/a15120460

Vancouver

Zvonarev N, Golyandina N. Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. Algorithms. 2022 Dec 5;15(12). 460. https://doi.org/10.3390/a15120460

Author

Zvonarev, Nikita ; Golyandina, Nina. / Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. In: Algorithms. 2022 ; Vol. 15, No. 12.

BibTeX

@article{e76b9f8e1cd7486e99426e50d94afca6,
title = "Mixed Alternating Projections with Application to Hankel Low-Rank Approximation",
abstract = "The method of alternating projections for extracting low-rank signals is considered. The problem of decreasing the computational costs while keeping the estimation accuracy is analyzed. The proposed algorithm consists of alternating projections on the set of low-rank matrices and the set of Hankel matrices, where iterations of weighted projections with different weights are mixed. For algorithm justification, theory related to mixed alternating projections to linear subspaces is studied and the limit of mixed projections is obtained. The proposed approach is applied to the problem of Hankel low-rank approximation for constructing a modification of the Cadzow algorithm. Numerical examples compare the accuracy and computational cost of the proposed algorithm and Cadzow iterations.",
keywords = "Structured low-rank approximation, alternating projection, singular spectrum analysis, Cadzow iterations, structured low-rank approximation",
author = "Nikita Zvonarev and Nina Golyandina",
note = "Zvonarev, N.; Golyandina, N. Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. Algorithms 2022, 15, 460. https://doi.org/10.3390/a15120460",
year = "2022",
month = dec,
day = "5",
doi = "10.3390/a15120460",
language = "English",
volume = "15",
journal = "Algorithms",
issn = "1999-4893",
publisher = "MDPI AG",
number = "12",

}

RIS

TY - JOUR

T1 - Mixed Alternating Projections with Application to Hankel Low-Rank Approximation

AU - Zvonarev, Nikita

AU - Golyandina, Nina

N1 - Zvonarev, N.; Golyandina, N. Mixed Alternating Projections with Application to Hankel Low-Rank Approximation. Algorithms 2022, 15, 460. https://doi.org/10.3390/a15120460

PY - 2022/12/5

Y1 - 2022/12/5

N2 - The method of alternating projections for extracting low-rank signals is considered. The problem of decreasing the computational costs while keeping the estimation accuracy is analyzed. The proposed algorithm consists of alternating projections on the set of low-rank matrices and the set of Hankel matrices, where iterations of weighted projections with different weights are mixed. For algorithm justification, theory related to mixed alternating projections to linear subspaces is studied and the limit of mixed projections is obtained. The proposed approach is applied to the problem of Hankel low-rank approximation for constructing a modification of the Cadzow algorithm. Numerical examples compare the accuracy and computational cost of the proposed algorithm and Cadzow iterations.

AB - The method of alternating projections for extracting low-rank signals is considered. The problem of decreasing the computational costs while keeping the estimation accuracy is analyzed. The proposed algorithm consists of alternating projections on the set of low-rank matrices and the set of Hankel matrices, where iterations of weighted projections with different weights are mixed. For algorithm justification, theory related to mixed alternating projections to linear subspaces is studied and the limit of mixed projections is obtained. The proposed approach is applied to the problem of Hankel low-rank approximation for constructing a modification of the Cadzow algorithm. Numerical examples compare the accuracy and computational cost of the proposed algorithm and Cadzow iterations.

KW - Structured low-rank approximation

KW - alternating projection

KW - singular spectrum analysis

KW - Cadzow iterations

KW - structured low-rank approximation

UR - https://www.mendeley.com/catalogue/26692e94-d422-3d16-aa2f-b31f65b837fc/

U2 - 10.3390/a15120460

DO - 10.3390/a15120460

M3 - Article

VL - 15

JO - Algorithms

JF - Algorithms

SN - 1999-4893

IS - 12

M1 - 460

ER -

ID: 100828545