This paper presents a new CG-type algorithm for solving large linear systems. It isobtained from a subclass of the ABS algorithm-Voyevodin’s CG method by choosingthe parameter matrix B in some special ways. Having pr...This paper presents a new CG-type algorithm for solving large linear systems. It isobtained from a subclass of the ABS algorithm-Voyevodin’s CG method by choosingthe parameter matrix B in some special ways. Having preconditioning properties, thematrix B makes the new algorithm converge fast. The convergence analysis is given.Several ways for choosing B, which are similar to the polynomial preconditioing, arediscussed. Numerical tests indicate that the new algorithm is effective and competitive.Besides, it is suitable for parallel architectectures.展开更多
文摘This paper presents a new CG-type algorithm for solving large linear systems. It isobtained from a subclass of the ABS algorithm-Voyevodin’s CG method by choosingthe parameter matrix B in some special ways. Having preconditioning properties, thematrix B makes the new algorithm converge fast. The convergence analysis is given.Several ways for choosing B, which are similar to the polynomial preconditioing, arediscussed. Numerical tests indicate that the new algorithm is effective and competitive.Besides, it is suitable for parallel architectectures.