NDLI: A parallel solving method for block-tridiagonal equations on CPU

Content Provider	Springer Nature Link
Author	Yang, Wangdong Li, Kenli Li, Keqin
Copyright Year	2016
Abstract	Solving block-tridiagonal systems is one of the key issues in numerical simulations of many scientific and engineering problems. Non-zero elements are mainly concentrated in the blocks on the main diagonal for most block-tridiagonal matrices, and the blocks above and below the main diagonal have little non-zero elements. Therefore, we present a solving method which mixes direct and iterative methods. In our method, the submatrices on the main diagonal are solved by the direct methods in the iteration processes. Because the approximate solutions obtained by the direct methods are closer to the exact solutions, the convergence speed of solving the block-tridiagonal system of linear equations can be improved. Some direct methods have good performance in solving small-scale equations, and the sub-equations can be solved in parallel. We present an improved algorithm to solve the sub-equations by thread blocks on GPU, and the intermediate data are stored in shared memory, so as to significantly reduce the latency of memory access. Furthermore, we analyze cloud resources scheduling model and obtain ten block-tridiagonal matrices which are produced by the simulation of the cloud-computing system. The computing performance of solving these block-tridiagonal systems of linear equations can be improved using our method.
Starting Page	1760
Ending Page	1781
Page Count	22
File Format	PDF
ISSN	09208542
Journal	The Journal of Supercomputing
Volume Number	73
Issue Number	5
e-ISSN	15730484
Language	English
Publisher	Springer US
Publisher Date	2016-09-22
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Block tridiagonal Linear equations Sparse matrix-vector multiplication Solving Programming Languages, Compilers, Interpreters Processor Architectures Computer Science
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Information Systems Hardware and Architecture Software

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