Journal of Mathematical Modelling and Algorithms

, Volume 2, Issue 3, pp 217-234

First online:

Efficient and Optimal Parallel Algorithms for Cholesky Decomposition

  • Eunice E. SantosAffiliated withDepartment of Computer Science, Virginia Polytechnic Institute & State University
  • , Pei-Yue ChuAffiliated withDepartment of Computer Science and Engineering, Lehigh University

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In this paper, we consider the problem of developing efficient and optimal parallel algorithms for Cholesky decomposition. We design our algorithms based on different data layouts and methods. We thereotically analyze the run-time of each algorithm. In order to determine the optimality of the algorithms designed, we derive theoretical lower bounds on running time based on initial data layout and compare them against the algorithmic run-times. To address portability, we design our algorithms and perform complexity analysis on the LogP model. Lastly, we implement our algorithms and analyze performance data.

Cholesky decomposition parallel complexity algorithms and complexity LogP model numerical linear algebra