Rank k Cholesky Up/Down-dating on the GPU: gpucholmodV0.2

TL;DR

This paper presents a GPU-based algorithm for rank-k Cholesky updates and downdates, achieving significant speedups over CPU implementations for large matrices by leveraging CUDA and GPU parallelism.

Contribution

The authors introduce a GPU-accelerated method for rank-k Cholesky modifications that reduces computation time and scales efficiently with matrix size, using CUDA and multiple kernels.

Findings

Achieves around 7x speedup for 5000x5000 matrices with k=16.

Handles larger problems due to O(n) GPU memory scaling.

Limited speedups due to bandwidth-bound nature of the problem.

Abstract

In this note we briefly describe our Cholesky modification algorithm for streaming multiprocessor architectures. Our implementation is available in C++ with Matlab binding, using CUDA to utilise the graphics processing unit (GPU). Limited speed ups are possible due to the bandwidth bound nature of the problem. Furthermore, a complex dependency pattern must be obeyed, requiring multiple kernels to be launched. Nonetheless, this makes for an interesting problem, and our approach can reduce the computation time by a factor of around 7 for matrices of size 5000 by 5000 and k=16, in comparison with the LINPACK suite running on a CPU of comparable vintage. Much larger problems can be handled however due to the O(n) scaling in required GPU memory of our method.