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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.14596 |
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| _version_ | 1866910701519372288 |
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| author | Jiang, Xin Nguyen, Edward Duc Hien Uribe, César A. Ying, Bicheng |
| author_facet | Jiang, Xin Nguyen, Edward Duc Hien Uribe, César A. Ying, Bicheng |
| contents | In this paper, we study sparse factorization of the (scaled) square all-ones matrix $J$ of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of $J$: the reduced hierarchically banded (RHB) factorization and the doubly stochastic hierarchically banded (DSHB) factorization. Based on the DSHB factorization, we propose the sequential doubly stochastic (SDS) factorization, in which~$J$ is decomposed as a product of sparse, doubly stochastic matrices. Finally, we discuss the application of the proposed sparse factorizations to the decentralized average consensus problem and decentralized optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14596 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse factorization of the square all-ones matrix of arbitrary order Jiang, Xin Nguyen, Edward Duc Hien Uribe, César A. Ying, Bicheng Optimization and Control In this paper, we study sparse factorization of the (scaled) square all-ones matrix $J$ of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of $J$: the reduced hierarchically banded (RHB) factorization and the doubly stochastic hierarchically banded (DSHB) factorization. Based on the DSHB factorization, we propose the sequential doubly stochastic (SDS) factorization, in which~$J$ is decomposed as a product of sparse, doubly stochastic matrices. Finally, we discuss the application of the proposed sparse factorizations to the decentralized average consensus problem and decentralized optimization. |
| title | Sparse factorization of the square all-ones matrix of arbitrary order |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.14596 |