期刊
IEEE TRANSACTIONS ON SERVICES COMPUTING
卷 15, 期 4, 页码 1967-1979出版社
IEEE COMPUTER SOC
DOI: 10.1109/TSC.2020.3027580
关键词
Big Data; Sparse matrices; Linear regression; Linear systems; Iterative methods; Mathematical model; Matrix decomposition; Kaczmarz algorithm; random iterations; matrix factorization; tremendous linear systems; big data
This paper proposes a new divide-and-iterate framework for efficient processing of big-data matrices and solving large linear systems of equations using factored matrices. The convergence of the new iterative algorithms is rigorously proved, and the time and memory complexities are studied to demonstrate the resource efficiency of the proposed algorithms. Numerical experiments are conducted to illustrate the effectiveness of the new framework.
Matrix calculations are often required for the analysis of any big-data cloud computing system. It is quite common to process big-data associated matrices possessing the sparsity and low-rank properties. In order to efficiently deal with big-data matrices, we propose a new divide-and-iterate framework, which can be invoked to solve an enormously large linear system of equations by taking advantage of factored matrices. The Kaczmarz algorithm (KA) is utilized here to design the parallel iterative algorithms which are capable of solving a large system of equations by iteratively updating the solution through the reduction into the factorized subsystems in parallel. The convergences of our proposed new iterative algorithms are justified by the rigorous proofs. Besides, the time- and memory-complexities are studied to demonstrate the resource efficiency of the proposed algorithms. Numerical experiments are also presented to illustrate the effectiveness of this proposed new framework.
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