Projection Improved SPAI Preconditioner for FGMRES  

作　　者：Mingguang Geng Shuli Sun 

机构地区：[1]LTCS,Department of Mechanics and Engineering Science,College of Engineering,Peking University,Beijing 100871,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第4期1035-1052,共18页高等学校计算数学学报（英文版）

基　　金：supported by the National Key R&D Program of China(Grant No.2021YFB2401700);the National Natural Science Foundation of China(Grant No.11672362).

摘　　要：Krylov subspace methods are widely used for solving sparse linear algebraic equations,but they rely heavily on preconditioners,and it is difficult to find an effective preconditioner that is efficient and stable for all problems.In this paper,a novel projection strategy including the orthogonal and the oblique projection is proposed to improve the preconditioner,which can enhance the efficiency and stability of iteration.The proposed strategy can be considered as a minimization process,where the orthogonal projection minimizes the energy norm of error and the oblique projection minimizes the 2-norm of the residual,meanwhile they can be regarded as approaches to correct the approximation by solving low-rank inverse of the matrices.The strategy is a wide-ranging approach and provides a way to transform the constant preconditioner into a variable one.The paper discusses in detail the projection strategy for sparse approximate inverse(SPAI)preconditioner applied to flexible GMRES and conducts the numerical test for problems from different applications.The results show that the proposed projection strategy can significantly improve the solving process,especially for some non-converging and slowly convergence systems.

关 键 词：Generalized minimal residual PRECONDITIONER sparse approximate inverse oblique projection orthogonal projection 

分 类 号：O17[理学—数学]