Solver Selection For Large Linear Systems

Numerical simulation processes in scientific and engineering applications require efficient solution of large sparse linear systems,and finding a faster and more accurate solver for linear systems is becoming the core task of the research in scientific computing.Therefore,it is instructive to select a better solver intelligently among a solver set before applying it to solve a linear system.To explore this research,the database for training models is constructed in this paper according to performance of different solvers and coefficient matrix features of various linear systems.Multiple machine learning models are employed to construct a mapping between linear systems and candidate solvers for solver selection,which require computation and data mining for coefficient matrix features of linear systems.However,it is quite complicated to compute certain matrix features.In this thesis,a new selection strategy for matrix features is proposed to reduce computational cost,and a higher prediction accuracy is achieved compared with the existing strategy.The GMRES-type and BiCG-type solvers are selected for the numerical experiments as the solver library.The experimental results show that construction time for most classifiers is reduced by 40%at least,but more than 90%prediction accuracy on GMRES-type solvers and 85%prediction accuracy on BiCG-type solvers can be reached.