Multisplitting and two stage multisplitting of a symmetric positive definite matrix^∗

^∗Supported by the State Major Key Project for Basic Researches and Doctorial Point Foundation of China.

Abstract

To solve the symmetric positive definite linear system Ax = b on parallel and vector machines, both multisplitting methods and two-stage multisplitting methods are considered. Here the s.p.d. (symmetric positive definite) matrix A need not be assumed in a special form (e.g., the dissection form [11]). The main tool for deriving our methods is the diagonally compensated reduction (cf. [1]). The convergence of such two methods is also discussed by using this tool.

Keywords:

• Diagonally compensated reduction
• two-stage
• multisplitting

C.R. Category:

• G.1.3

^∗Supported by the State Major Key Project for Basic Researches and Doctorial Point Foundation of China.

^∗Supported by the State Major Key Project for Basic Researches and Doctorial Point Foundation of China.

Notes

^∗Supported by the State Major Key Project for Basic Researches and Doctorial Point Foundation of China.