A high performance implementation of Zolo-SVD algorithm on distributed memory systems

Abstract

This paper introduces a high performance implementation of the Zolo-SVD algorithm on distributed memory systems, which is based on the polar decomposition (PD) algorithm via the Zolotarev’s function (Zolo-PD), originally proposed by Nakatsukasa and Freund [SIAM Review, 2016]. Our implementation highly relies on the routines of ScaLAPACK and therefore it is portable. Compared with the other PD algorithms such as the QR-based dynamically weighted Halley method (QDWH-PD), Zolo-PD is naturally parallelizable and has better scalability though performs more floating-point operations. When using many processors, Zolo-PD is usually 1.20 times faster than the QDWH-PD algorithm, and Zolo-SVD can be about two times faster than the ScaLAPACK routine PDGESVD. These numerical experiments are performed on Tianhe-2A supercomputer, one of the fastest supercomputers in the world, and the tested matrices include some sparse matrices from particular applications and some randomly generated dense matrices with different dimensions. Our QDWH-SVD and Zolo-SVD implementations are freely available at https://github.com/shengguolsg/Zolo-SVD.