This paper deals with solving a class of three-by-three block saddle point problems. The systems are solved by preconditioning techniques. Based on an iterative method, we construct upper triangular preconditioner. convergence the presented method is studied in details. Finally, some numerical experiments given to demonstrate superiority proposed preconditioner over existing ones.

We have defined and analyzed a semi-Toeplitz preconditioner for timedependent and steady-state convection-diffusion problems. The preconditioner exhibits very good theoretical convergence properties. The analysis is corroborated by numerical experiments.

Several problems in early vision have been formulated in the past in a regularization framework. These problems, when discretized, lead to large sparse linear systems. In this paper, we present a novel physically based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to dramatically improve the speed of convergence for solving the aforement...

Incomplete LDL factorizations sometimes produce an indefinite preconditioner evenwhen the input matrix is Hermitian positive definite. The two most popular iterative solvers for symmetric systems, CG and MINRES, cannot use such preconditioners; they require a positive definite preconditioner. One approach, that has been extensively studied to address this problem is to force positive definitene...

We study the performance of a new block preconditioner for class \(3\times 3\) saddle point problems which arise from finite-element methods solving time-dependent Maxwell equations and some other practical problems. also estimate lower upper bounds eigenvalues preconditioned matrix. Finally, we examine our to accelerate convergence speed GMRES method shows effectiveness preconditioner.

Lower bounds for the condition numbers of the preconditioned systems are obtained for the Bramble-Pasciak-Schatz substructuring preconditioner and the Neumann-Neumann preconditioner in two dimensions. They show that the known upper bounds are sharp.

We introduce a method for constructing an element-by-element sparse approximate inverse (SAI) preconditioner designed to be effective in a massively-parallel spectral element modeling environment involving nonsymmetric systems. This new preconditioning approach is based on a spectral optimization of a low-resolution preconditioned system matrix (PSM). We show that the local preconditioning matr...

We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, ...

A convergence theory is presented for a substructuring preconditioner based on constrained energy minimization concepts. The preconditioner is formulated as an Additive Schwarz method and analyzed by building on existing results for Balancing Domain Decomposition. The main result is a bound on the condition number based on inequalities involving the matrices of the preconditioner. Estimates of ...