The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered th...The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered the preferred methods. Selecting an effective preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The purpose of this paper is to predict the parameter solvability space of the preconditioners with two or more parameters. The parameter solvability space is usually irregular, however, in many situations it shows spatial locality, i.e. the parameter locations that are closer in parameter space are more likely to have similar solvability. We propose three spatial data mining methods to predict the solvability of ILUT which make usage of spatial locality in different ways. The three methods are MSC （multi-points SVM classifier）, OSC （overall SVM classifier）, and OSAC （overall spatial autoregressive classifier）. The experimental results show that both MSC and OSAC can obtain 90% accuracy in prediction, but OSAC is much simpler to implement. We focus our work on ILUT preconditioner [2], but the proposed strategies should be applicable to other preconditioners with two or more parameters.展开更多
文摘The solution of large sparse linear systems is one of the most important problems in large scale scientific computing. Among the many methods developed, the preconditioned Krylov subspace methods [1] are considered the preferred methods. Selecting an effective preconditioner with appropriate parameters for a specific sparse linear system presents a challenging task for many application scientists and engineers who have little knowledge of preconditioned iterative methods. The purpose of this paper is to predict the parameter solvability space of the preconditioners with two or more parameters. The parameter solvability space is usually irregular, however, in many situations it shows spatial locality, i.e. the parameter locations that are closer in parameter space are more likely to have similar solvability. We propose three spatial data mining methods to predict the solvability of ILUT which make usage of spatial locality in different ways. The three methods are MSC （multi-points SVM classifier）, OSC （overall SVM classifier）, and OSAC （overall spatial autoregressive classifier）. The experimental results show that both MSC and OSAC can obtain 90% accuracy in prediction, but OSAC is much simpler to implement. We focus our work on ILUT preconditioner [2], but the proposed strategies should be applicable to other preconditioners with two or more parameters.
