A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

AbRtract This paper deals with the domain decomposition-based preconditioned conjugate gradient method. The Schur complement is expressed as a function of & simple interface matrix. This function is approximated by a simple rational function to generate a simple matrix that is then used 8.8 & preconditioner for the Schur complement. Extensive experiments are performed to examine the effectivene...

The present paper is devoted to an improvement of the theory of the recently proposed generalized augmented matrix preconditioning method [5]. Namely, we compute a sharp lower bound on eigenvalues of the preconditioned matrix based on the properties of the projector involved in its definition.

We show that sparse spherical harmonic expansions can be recovered from a small number of randomly chosen samples on the sphere using `1-minimization. To this end, we establish the restricted isometry property of an associated preconditioned random measurement matrix.

Mesenchymal stem cells (MSCs) are widely considered for treatment of pulmonary fibrosis based on the anti-inflammatory, antifibrotic, antiapoptotic, and regenerative properties of the cells. Recently, elevated levels of oncostatin M (OSM) have been reported in the bronchoalveolar lavage fluid of a pulmonary fibrosis animal model and in patients. In this work, we aimed to prolong engrafted MSC s...

In this paper we consider the computation of an eigenvalue and corresponding eigenvector of a large sparse Hermitian positive definite matrix using inexact inverse iteration with a fixed shift. For such problems the large sparse linear systems arising at each iteration are often solved approximately by means of symmetrically preconditioned MINRES. We consider preconditioners based on the incomp...

In this paper, a new preconditioned AOR iterative method is proposed with the preconditioner I + Sα. Some comparison theorems are given when the coefficient matrix A of linear system is an irreducible L− matrix. Numerical example shows that our methods are superior to the basic AOR iterative method.

A preconditioned SSOR iterative method with a multi-parameters preconditioner I + S̃α is proposed. Some convergence and comparison results for αi ∈ [0, 1] are given when the coefficient matrix of linear system A is a nonsingular M−matrix. Numerical example shows that our methods are superior to the basic SSOR iterative method.

A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

A relaxed splitting preconditioner based on matrix splitting is introduced in this paper for linear systems of saddle point problem arising from numerical solution of the incompressible NavierStokes equations. Spectral analysis of the preconditioned matrix is presented, and numerical experiments are carried out to illustrate the convergence behavior of the preconditioner for solving both steady...