Predicting the solvability space of the preconditioned krylov subspace methods

In this paper we predict the parameter solvability space of the preconditioned Krylov subspace methods 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 methods to predict the solvability of ILUT which make usage of spatial locality in different ways. The three methods are multi-points SVM classifier (MSC), overall SVM classifier (OSC), and Overall Spatial Autoregressive Classifier (OSAC). 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 [6], but the proposed strategies should be applicable to other preconditioners with two or more parameters. Copyright ISCA.