View in EDS

Mixed-Precision Orthogonalization-Free Projection Methods for Eigenvalue and Singular Value Problems.

Saved in:
Bibliographic Details
Title: Mixed-Precision Orthogonalization-Free Projection Methods for Eigenvalue and Singular Value Problems.
Authors: Xu, Tianshi1 (AUTHOR) tianshi.xu@emory.edu, Zhang, Zechen2 (AUTHOR) zhan5260@umn.edu, Chen, Jie3 (AUTHOR) jiechenj@amazon.com, Saad, Yousef2 (AUTHOR) saad@umn.ed, Xi, Yuanzhe1 (AUTHOR) yuanzhe.xi@emory.edu
Source: SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pB544-B568. 25p.
Subjects: Eigenvalues, Singular value decomposition, Arithmetic, Rayleigh-Ritz method, Linear dependence (Mathematics), Matrices (Mathematics), Orthogonalization
Abstract: Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and the singular value decomposition remains challenging. This paper introduces an approach that eliminates orthogonalization requirements in traditional Rayleigh–Ritz projection methods. The proposed method employs nonorthogonal bases computed at reduced precision, resulting in bases computed without inner products. A primary focus is on maintaining the linear independence of the basis vectors. Through extensive evaluation with both synthetic test cases and real-world applications, we demonstrate that the proposed approach achieves the desired accuracy while fully taking advantage of mixed-precision arithmetic. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Description
Abstract:Mixed-precision arithmetic offers significant computational advantages for large-scale matrix computation tasks, yet preserving accuracy and stability in eigenvalue problems and the singular value decomposition remains challenging. This paper introduces an approach that eliminates orthogonalization requirements in traditional Rayleigh–Ritz projection methods. The proposed method employs nonorthogonal bases computed at reduced precision, resulting in bases computed without inner products. A primary focus is on maintaining the linear independence of the basis vectors. Through extensive evaluation with both synthetic test cases and real-world applications, we demonstrate that the proposed approach achieves the desired accuracy while fully taking advantage of mixed-precision arithmetic. [ABSTRACT FROM AUTHOR]
ISSN:10648275
DOI:10.1137/25M1756922