Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
Changing the norm in conjugate gradient type algorithms
SIAM Journal on Numerical Analysis
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioned AHSS iteration method for singular saddle point problems
Numerical Algorithms
On generalized parameterized inexact Uzawa method for a block two-by-two linear system
Journal of Computational and Applied Mathematics
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems
Computers & Mathematics with Applications
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The restrictively preconditioned conjugate gradient (RPCG) method for solving large sparse system of linear equations of a symmetric positive definite and block two-by-two coefficient matrix is further studied. In fact, this RPCG method is essentially the classical preconditioned conjugate gradient (PCG) method with a specially structured preconditioner. Within this setting, we present algorithmic descriptions of two restrictive preconditioners that, respectively, employ the block Jacobi and the block symmetric Gauss-Seidel matrix splitting matrices as approximations to certain matrices involved in them, and give convergence analyses of the correspondingly induced two PCG methods. Numerical results show that these restrictive preconditioners can lead to practical and effective PCG methods for solving large sparse systems of linear equations of symmetric positive definite and block two-by-two coefficient matrices.