A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU–GPU parallelism are discussed.

💡 Research Summary

The paper presents a novel GPU‑accelerated algorithm for computing the hyperbolic singular value decomposition (HSVD) using a one‑sided Jacobi scheme. HSVD differs from the conventional SVD in that it employs hyperbolic rotations, which can simultaneously handle singular values of opposite signs and are essential for solving symmetric indefinite eigenvalue problems. The authors redesign the classic Jacobi HSVD to exploit the massive parallelism, memory hierarchy, and warp‑level synchronization capabilities of modern graphics processing units.

In the algorithmic core, each GPU thread block is assigned a pair of matrix rows (or columns) according to a deterministic pairing schedule (e.g., cyclic shift). For a given pair, the block first computes the inner product and norms using warp‑wide reductions, then derives the hyperbolic rotation parameters (α, β) that zero out the off‑diagonal element. The rotation matrix has the form

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