UnifaSVD: A Unified and Fast Framework of Singular Value Decomposition on GPU Architectures

Singular value decomposition (SVD) is a fundamental matrix factorization in scientific computing and data analysis, but computing it efficiently on modern GPUs remains challenging. Full SVD provides strong numerical robustness but is often expensive for large matrices, whereas randomized SVD (RSVD) improves performance but may exhibit accuracy variability, especially when the target rank is unknown or the singular spectrum decays slowly. To address this challenge, we propose UnifaSVD, a unified and adaptive framework for high-performance and numerically reliable SVD on GPUs. UnifaSVD combines a numerically stable Householder QB (HQB) factorization for numerical rank estimation with a unified EVD-based SVD backend for efficient computation of the required singular values and vectors. Its adaptive architecture supports full-rank, low-rank, and unknown-rank matrices by dynamically selecting an appropriate computational path according to matrix characteristics and user-specified numerical requirements. Rather than relying on a fixed decomposition strategy, UnifaSVD integrates efficient factorization, adaptive rank handling, and lightweight refinement within a single framework. Experimental results show that UnifaSVD achieves numerical accuracy close to full SVD while delivering substantially higher performance across a wide range of tested cases. By automating algorithm selection based on matrix properties and numerical requirements, UnifaSVD provides a robust and efficient solution for SVD on modern GPU architectures.