A High-Performance Preconditioned SVD Solver for Accurately Computing Large-Scale Singular Value Problems in PRIMME
Student: Lingfei Wu (William & Mary)
Supervisor: Andreas Stathopoulos (College of William & Mary)
Abstract: The dramatic increase in the demand for solving large scale singular value problems has rekindled interest in iterative methods for the SVD. Unlike the remarkable progress in dense SVD solvers, some promising recent advances in large scale iterative methods are still plagued by slow convergence and accuracy limitations for computing smallest singular triplets. Furthermore, their current implementations in MATLAB cannot address the required large problems. Recently, we presented a preconditioned, two-stage method to effectively and accurately compute a small number of extreme singular triplets. In this research, we present a high-performance software, PRIMME_SVDS, that implements our hybrid method based on the state-of-the-art eigensolver package PRIMME for both largest and smallest singular values. PRIMME_SVDS fills a gap in production level software for computing the partial SVD, especially with preconditioning. The numerical experiments demonstrate its superior performance compared to other state-of-the-art methods and its good scalability performance under strong and weak scaling.
Two-page extended abstract: pdf