A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
A class of hybrid algebraic multilevel preconditioning methods are presented for solving the systems of linear equations with symmetric positive definite matrices resulting from the discretization of many second orde...A class of hybrid algebraic multilevel preconditioning methods are presented for solving the systems of linear equations with symmetric positive definite matrices resulting from the discretization of many second order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexities for 2-D and 3-D problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.1980 Mathematics Subject Classification (1985 Revision ). AMS (MOS ): 65F10,65N20, 65N301 CR:Gl. 3.展开更多
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘A class of hybrid algebraic multilevel preconditioning methods are presented for solving the systems of linear equations with symmetric positive definite matrices resulting from the discretization of many second order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexities for 2-D and 3-D problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.1980 Mathematics Subject Classification (1985 Revision ). AMS (MOS ): 65F10,65N20, 65N301 CR:Gl. 3.
