Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems

doi:10.1007/s10915-023-02447-4

	Double Precision is not Necessary for LSQR for Solving Discrete Linear Ill-Posed Problems
	Li, Haibo
	2024-03-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING
ISSN	0885-7474
卷号	98 期号:3 页码:30
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.
关键词	Mixed precision Linear ill-posed problem Regularization LSQR Roundoff unit Semi-convergence
DOI	10.1007/s10915-023-02447-4
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[3192270206]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001154181300002
出版者	SPRINGER/PLENUM PUBLISHERS
引用统计
文献类型	期刊论文
条目标识符	http://119.78.100.204/handle/2XEOYT63/38364
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.