Vectorization of some block preconditioning conjugate gradient methods (Q749152)

Although the preconditioned conjugate gradient methods are effective for solving the linear systems arising from discretization of elliptic partial differential equations, the solution of the linear system \(Mr=s\), \(M=LD^{-1}L^ T\), where D, L are, respectively, diagonal and bidiagonal block matrices, to get the preconditioned residual, is a quite difficult task when using vector processors. A modified algorithm leading to better performances is discussed. Three numerical tests carried out on a single processor of a CRAY X-MP/48 are presented as a numerical evidence.