High-performance parallel and distributed computing for the BMI eigenvalue problem

The BMI Eigenvalue Problem is one of optimization problems and is to minimize the greatest eigenvalue or a bilinear matrix function. This paper proposes a parallel algorithm to compute the ϵ-optimal solution of the BMI Eigenvalue Problem on parallel and distributed computing systems. The proposed algorithm performs a parallel branch and bound method to compute the e-optimal solution using the Master-Worker paradigm. The performance evaluation results on PC clusters and a Grid computing system showed that the proposed algorithm reduced computation time of the BMI Eigenvalue problem to 1/91 of the sequential computation time on. a PC cluster with 128CPUs and reduced that to 1/7 on a Grid computing system. The results also showed that tuning of the computational granularity on a worker was required to achieve the best performance on a Grid computing system.