Search for Sparse Solutions of Super-Large Systems with a Tensor Structure

The problem of finding a sparse solution to large systems of linear equations arises in many applications related to signal processing. Sometimes, the size of these systems is so large that the known methods are inefficient. Such systems can be solved only if there is additional structure inherent i...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2022-11, Vol.62 (11), p.1782-1798
Main Authors: Zheltkov, D. A., Zamarashkin, N. L., Morozov, S. V.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
General Numerical Methods
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Signal processing
Tensors
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Summary:The problem of finding a sparse solution to large systems of linear equations arises in many applications related to signal processing. Sometimes, the size of these systems is so large that the known methods are inefficient. Such systems can be solved only if there is additional structure inherent in them. In this paper, an efficient approach for finding sparse solutions to super-large systems of linear equations with a tensor structure of a certain type is proposed. The theoretical analysis and experimental results make it possible to judge the efficiency of the proposed method.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542522110136