Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems
文献类型：期刊论文
| 作者 | Li, Haibo |
| 刊名 | JOURNAL OF SCIENTIFIC COMPUTING
 |
| 出版日期 | 2024-03-01 |
| 卷号 | 98期号:3页码:30 |
| 关键词 | Mixed precision Linear ill-posed problem Regularization LSQR Roundoff unit Semi-convergence |
| ISSN号 | 0885-7474 |
| DOI | 10.1007/s10915-023-02447-4 |
| 英文摘要 | The growing availability and usage of low precision floating point formats attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. In this paper we investigate the possibility of exploiting mixed precision computing in LSQR for solving discrete linear ill-posed problems. Based on the commonly used regularization model for linear inverse problems, we analyze the choice of proper computing precision in the two main parts of LSQR, including the construction of Krylov subspace and updating procedure of iterative solutions. We show that, under some mild conditions, the Lanczos vectors can be computed using single precision without loss of any accuracy of the final regularized solution as long as the noise level is not extremely small. We also show that the most time consuming part for updating iterative solutions can be performed using single precision without sacrificing any accuracy. The results indicate that several highly time consuming parts of the algorithm can be implemented using lower precisions, and provide a theoretical guideline for implementing a robust and efficient mixed precision variant of LSQR for solving discrete linear ill-posed problems. Numerical experiments are made to test two mixed precision variants of LSQR and confirming our results. |
| 资助项目 | National Natural Science Foundation of China[3192270206] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:001154181300002 |
| 出版者 | SPRINGER/PLENUM PUBLISHERS |
| 源URL | [http://119.78.100.204/handle/2XEOYT63/38363]  |
| 专题 | 中国科学院计算技术研究所期刊论文_英文 |
| 通讯作者 | Li, Haibo |
| 作者单位 | Chinese Acad Sci, Inst Comp Technol, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Haibo. Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems[J]. JOURNAL OF SCIENTIFIC COMPUTING,2024,98(3):30. |
| APA | Li, Haibo.(2024).Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems.JOURNAL OF SCIENTIFIC COMPUTING,98(3),30. |
| MLA | Li, Haibo."Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems".JOURNAL OF SCIENTIFIC COMPUTING 98.3(2024):30. |
入库方式： OAI收割
来源：计算技术研究所
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