Showing papers by "Zhong-Zhi Bai published in 2017"
TL;DR: Numerical results exhibit that the diagonal and circulant splitting preconditioner can significantly improve the convergence properties of GMRES and BiCGSTAB, and these precONDitioned Krylov subspace iteration methods outperform the conjugate gradient method preconditionsed by the approximate inversecirculant‐plus‐diagonal preconditiouser proposed recently by Ng and Pan.
52 citations
TL;DR: Numerical results on saddle-point linear systems arising from the discretization of a Stokes problem and of a distributed control problem show that good performance can be achieved when using inexact variants of the proposed preconditioners.
Abstract: We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding preconditioned matrix. Inexact variants are also considered. Numerical results on saddle-point linear systems arising from the discretization of a Stokes problem and of a distributed control problem show that good performance can be achieved when using inexact variants of the proposed preconditioners.
45 citations
TL;DR: Two iterative methods are described, that employ modulus-based iterative Methods, to compute approximate solutions in the nonnegative cone of large-scale Tikhonov regularization problems, and the structure of certain image restoration problems is explored.
28 citations
TL;DR: Numerical results indicate that the modulus‐based multigrid methods of the W‐cycle can achieve optimality in terms of both convergence factor and computing time, and their asymptotic convergence factors can be predicted perfectly by the local Fourier analysis of the corresponding modulus-based two‐grid methods.
Abstract: Summary
By employing modulus-based matrix splitting iteration methods as smoothers, we establish modulus-based multigrid methods for solving large sparse linear complementarity problems. The local Fourier analysis is used to quantitatively predict the asymptotic convergence factor of this class of multigrid methods. Numerical results indicate that the modulus-based multigrid methods of the W-cycle can achieve optimality in terms of both convergence factor and computing time, and their asymptotic convergence factors can be predicted perfectly by the local Fourier analysis of the corresponding modulus-based two-grid methods.
27 citations
TL;DR: For the Hermitian eigenproblems, this paper showed local cubic convergence of the inexact simplified Jacobi-Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration.
17 citations
TL;DR: This work proves local quadratic convergence of the inexact simplified Jacobi–Davidson method when the involved relaxed correction equation is solved by a standard Krylov subspace iteration, which particularly leads to local cubic convergence when the relaxed correction equations is solved to a prescribed precision proportional to the norm of the current residual.
15 citations
TL;DR: Numerical results show that the PRAVMM method is feasible and effective for solving the equality-constraint quadratic programming problems.
4 citations