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Mathematical Problems in Engineering
Volume 2017, Article ID 3021591, 11 pages
Research Article

Sparse Cholesky Factorization on FPGA Using Parameterized Model

School of Computer, National University of Defense Technology, Deya Road No. 109, Kaifu District, Changsha, Hunan 410073, China

Correspondence should be addressed to Yichun Sun; moc.621@nusnuhciy

Received 6 March 2017; Revised 19 August 2017; Accepted 12 September 2017; Published 17 October 2017

Academic Editor: Oleg V. Gendelman

Copyright © 2017 Yichun Sun et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cholesky factorization is a fundamental problem in most engineering and science computation applications. When dealing with a large sparse matrix, numerical decomposition consumes the most time. We present a vector architecture to parallelize numerical decomposition of Cholesky factorization. We construct an integrated analytical parameterized performance model to accurately predict the execution times of typical matrices under varying parameters. Our proposed approach is general for accelerator and limited by neither field-programmable gate arrays (FPGAs) nor application-specific integrated circuit. We implement a simplified module in FPGAs to prove the accuracy of the model. The experiments show that, for most cases, the performance differences between the predicted and measured execution are less than 10%. Based on the performance model, we optimize parameters and obtain a balance of resources and performance after analyzing the performance of varied parameter settings. Comparing with the state-of-the-art implementation in CPU and GPU, we find that the performance of the optimal parameters is 2x that of CPU. Our model offers several advantages, particularly in power consumption. It provides guidance for the design of future acceleration components.