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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.14341 |
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| _version_ | 1866915251427999744 |
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| author | Cheng, Cheng Sun, Qiyu Zheng, Cong |
| author_facet | Cheng, Cheng Sun, Qiyu Zheng, Cong |
| contents | Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose
iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm
and the conventional gradient descent algorithm
do. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Iterative Polynomial Approximation Algorithms for Inverse Graph Filters Cheng, Cheng Sun, Qiyu Zheng, Cong Signal Processing Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm and the conventional gradient descent algorithm do. |
| title | Iterative Polynomial Approximation Algorithms for Inverse Graph Filters |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2504.14341 |