Integrating adaptive optimization into least squares progressive iterative approximation
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913824896974848 |
|---|---|
| author | Sajavičius, Svajūnas |
| author_facet | Sajavičius, Svajūnas |
| contents | This paper introduces the Adaptive Gradient Least Squares Progressive iterative Approximation (AdagradLSPIA), an accelerated version of the Least Squares Progressive Iterative Approximation (LSPIA) method, enhanced with adaptive optimization techniques inspired by the adaptive gradient (Adagrad) algorithm. By using historical (accumulated) gradient information to dynamically adjust weights, AdagradLSPIA achieves faster convergence compared to the standard LSPIA method. The effectiveness of AdagradLSPIA is demonstrated through its application to tensor product B-spline surface fitting, where this method consistently outperforms LSPIA in terms of accuracy, computational efficiency, and robustness to variations in global weight selection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Integrating adaptive optimization into least squares progressive iterative approximation Sajavičius, Svajūnas Numerical Analysis This paper introduces the Adaptive Gradient Least Squares Progressive iterative Approximation (AdagradLSPIA), an accelerated version of the Least Squares Progressive Iterative Approximation (LSPIA) method, enhanced with adaptive optimization techniques inspired by the adaptive gradient (Adagrad) algorithm. By using historical (accumulated) gradient information to dynamically adjust weights, AdagradLSPIA achieves faster convergence compared to the standard LSPIA method. The effectiveness of AdagradLSPIA is demonstrated through its application to tensor product B-spline surface fitting, where this method consistently outperforms LSPIA in terms of accuracy, computational efficiency, and robustness to variations in global weight selection. |
| title | Integrating adaptive optimization into least squares progressive iterative approximation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2501.10170 |