Revisiting a Fast Newton Solver for a 2-D Spectral Estimation Problem: Computations with the Full Hessian
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908749610876928 |
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| author | Cheng, Ji Zhu, Bin |
| author_facet | Cheng, Ji Zhu, Bin |
| contents | Spectral estimation plays a fundamental role in frequency-domain identification and related signal processing problems. This paper revisits a 2-D spectral estimation problem formulated in terms of convex optimization. More precisely, we work with the dual optimization problem and show that the full Hessian of the dual function admits a Toeplitz-block Toeplitz structure which is consistent with our finding in a previous work. This particular structure of the Hessian enables a fast inversion algorithm in the solution of the dual optimization problem via Newton's method whose superior speed of convergence is illustrated via simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_02690 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Revisiting a Fast Newton Solver for a 2-D Spectral Estimation Problem: Computations with the Full Hessian Cheng, Ji Zhu, Bin Optimization and Control Spectral estimation plays a fundamental role in frequency-domain identification and related signal processing problems. This paper revisits a 2-D spectral estimation problem formulated in terms of convex optimization. More precisely, we work with the dual optimization problem and show that the full Hessian of the dual function admits a Toeplitz-block Toeplitz structure which is consistent with our finding in a previous work. This particular structure of the Hessian enables a fast inversion algorithm in the solution of the dual optimization problem via Newton's method whose superior speed of convergence is illustrated via simulations. |
| title | Revisiting a Fast Newton Solver for a 2-D Spectral Estimation Problem: Computations with the Full Hessian |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.02690 |