Enhanced Error Bounds For The Masked Projection Techniques via Cosine-Sine Decomposition
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910771435274240 |
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| author | Tripathi, Brij Nandan Shekhawat, Hanumant Singh |
| author_facet | Tripathi, Brij Nandan Shekhawat, Hanumant Singh |
| contents | The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often infeasible. This leads to the use of error-bound expressions in the literature. In this paper, we derive two generalized error bounds using cosine-sine decomposition for uniquely determined masked projection techniques. Generally, the masked projection technique is employed to efficiently approximate non-linear functions in the model reduction of dynamical systems. The discrete empirical interpolation method (DEIM) is also a masked projection technique; therefore, the proposed error bounds apply to DEIM projection errors. Furthermore, the proposed error bounds are shown tighter than those currently available in the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enhanced Error Bounds For The Masked Projection Techniques via Cosine-Sine Decomposition Tripathi, Brij Nandan Shekhawat, Hanumant Singh Numerical Analysis The masked projection techniques are popular in the area of non-linear model reduction. Quantifying and minimizing the error in model reduction, particularly from masked projections, is important. The exact error expressions are often infeasible. This leads to the use of error-bound expressions in the literature. In this paper, we derive two generalized error bounds using cosine-sine decomposition for uniquely determined masked projection techniques. Generally, the masked projection technique is employed to efficiently approximate non-linear functions in the model reduction of dynamical systems. The discrete empirical interpolation method (DEIM) is also a masked projection technique; therefore, the proposed error bounds apply to DEIM projection errors. Furthermore, the proposed error bounds are shown tighter than those currently available in the literature. |
| title | Enhanced Error Bounds For The Masked Projection Techniques via Cosine-Sine Decomposition |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.01651 |