| Autor: |
Fan, Yuwei, Guan, Haoran, Qiao, Zhonghua |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Shifted CholeskyQR3 is designed to address the QR factorization of ill-conditioned matrices. This algorithm introduces a shift parameter $s$ to prevent failure during the initial Cholesky factorization step. The choice of this shift parameter $s$ is critical for the algorithm's effectiveness. Our goal is to identify a smaller $s$ compared to the traditional selection involving $\|X\|_2$. In this research, we propose a new norm $\|X\|_g$, which is based on the column properties of $X$, to obtain a reduced shift parameter $s$ for the Shifted CholeskyQR3 algorithm. We provide rigorous proofs of orthogonality and residuals for the improved algorithm with our proposed $s$. Numerical experiments confirm the enhanced numerical stability of orthogonality and residuals with the reduced $s$. Furthermore, we compare CPU times with other algorithms to assess performance improvements. |
| Databáze: |
arXiv |
| Externí odkaz: |
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