Paper Info
Title
Implementing the Jacobi Algorithm for Solving Eigenvalues of Symmetric Matrices with CUDA
Abstract
Solving the eigenvalues of matrices is an open problem which is often related to scientific computation. With the increasing of the order of matrices, traditional sequential algorithms are unable to meet the needs for the calculation time. Although people can use cluster systems in a short time to solve the eigenvalues of large-scale matrices, it will bring an increase in equipment costs and power consumption. This paper proposes a parallel algorithm named Jacobi on gpu which is implemented by CUDA (Computer Unified Device Architecture) on GPU (Graphic Process Unit) to solve the eigenvalues of symmetric matrices. In our experimental environment, we have Intel Core i5-760 quad-core CPU, NVIDIA GeForce GTX460 card, and Win7 64-bit operating system. When the size of matrix is 10240×10240, the number of iterations is 10000 times, the speedup ratio is 13.71. As the size of matrices increase, the speedup ratio increases correspondingly. Moreover, as the number of iterations increases, the speedup ratio is very stable. When the size of matrix is 8192×8192, the number of iterations are 1000, 2000, 4000, 8000 and 16000 respectively, the standard deviation of the speedup ratio is 0.1161. The experimental results show that the Jacobi on gpu algorithm can save more running time than traditional sequential algorithms and the speedup ratio is 3.02~13.71. Therefore, the computing time of traditional sequential algorithms to solve the eigenvalues of matrices is reduced significantly.
Year
DOI
Venue
2012
10.1109/NAS.2012.12
NAS
Keywords
Field
DocType
large-scale matrices,eigenvalues,pattern clustering,computer unified device architecture,jacobi iteration,matrix eigenvalue,jacobi algorithm,gpu,speedup ratio increases correspondingly,cluster systems,sequential algorithms,symmetric matrix,iterations increase,graphic process unit,parallel architectures,graphics processing units,experimental environment,running time,cuda,mathematics computing,computing time,symmetric matrices,parallel algorithms,calculation time,win7 64-bit operating system,short time,speedup ratio,parallel algorithm,matrices increase,eigenvalues and eigenfunctions,intel core i5-760 quad-core cpu,jacobian matrices,nvidia geforce gtx460 card,traditional sequential algorithm,kernel,indexes
Jacobi method,Parallel algorithm,CUDA,Computer science,Matrix (mathematics),Parallel computing,Jacobi eigenvalue algorithm,Symmetric matrix,Eigenvalues and eigenvectors,Speedup
Conference
ISBN
Citations 
PageRank 
978-1-4673-1889-1
2
0.55
References 
Authors
3
7
Name
Order
Citations
PageRank
Tao Wang120.55
Longjiang Guo217726.73
Guilin Li3116.09
Jinbao Li425139.56
Renda Wang520.89
Meirui Ren6217.30
Jing (Selena) He712914.61