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