A Mixed Precision Jacobi SVD Algorithm

We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and then performs one-sided Jacobi rotations in the working precis...

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Bibliographic Details
Published inACM transactions on mathematical software Vol. 51; no. 1; pp. 1 - 33
Main Authors Gao, Weiguo, Ma, Yuxin, Shao, Meiyue
Format Journal Article
LanguageEnglish
Published New York, NY ACM 04.04.2025
Subjects
Computations on matrices
Mathematics of computing
mixed precision algorithm
high relative accuracy
Jacobi algorithm
Singular value decomposition
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ISSN0098-3500
1557-7295
1557-7295
DOI10.1145/3721124

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Summary:We propose a mixed precision Jacobi algorithm for computing the singular value decomposition (SVD) of a dense matrix. After appropriate preconditioning, the proposed algorithm computes the SVD in a lower precision as an initial guess and then performs one-sided Jacobi rotations in the working precision as iterative refinement. By carefully transforming a lower precision solution to a higher precision one, our algorithm achieves about \(2\times\) speedup on the x86-64 architecture compared to the usual one-sided Jacobi SVD algorithm in LAPACK, without sacrificing the accuracy.
ISSN:0098-3500
1557-7295
1557-7295
DOI:10.1145/3721124