Mixed precision thin SVD algorithms based on the Gram matrix
This work addresses computational efficiency for SVD in numerical linear algebra, offering significant speed improvements for applications involving tall-and-skinny matrices, though it appears incremental as it builds on existing Gram matrix and Jacobi techniques.
The paper tackles the problem of computing the singular value decomposition (SVD) for tall-and-skinny matrices by introducing a mixed precision algorithm based on the Gram matrix and Jacobi methods, achieving high relative accuracy and speedups of over 10x on a single CPU and about 2x on distributed systems compared to traditional methods.
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and coupling it with a Jacobi algorithm, our theoretical analysis and numerical experiments both indicate that the singular values computed by this mixed precision thin SVD algorithm attain high relative accuracy. In practice, our mixed precision thin SVD algorithm yields speedups of over 10x on a single CPU and about 2x on distributed memory systems when compared with traditional thin SVD methods.