A Two-Level Preconditioned Conjugate-Gradient Method in Distorted and Structured Grids

In this paper, we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topologically structured grid. The CPU time of this method is less than that of the multigrid preconditioned C-G method (MGCG) using the quadratic element, but their accuracy is almost the same. Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.     

Riemannian Trust-Region Method for the Maximal Correlation Problem

The maximal correlation problem (MCP) arising in the canonical correlation analysis is very important to assess the relationship between sets of random variables. Efficient and fast methods for solving MCP are desired in broad statistical and nonstatistical applications. Some early proposed algorithms are based on the first-order information of MCP, and fast convergence could not be expected. In this article, we turn the generic Riemannian trust-region method of Absil et al. [2 P.-A. Absil , C. G. Baker , and K. A. Gallivan ( 2007 ). Trust-region methods on Riemannian manifolds . Found. Comput. Math. 7 : 303 – 330 . [Google Scholar]] into a practical algorithm for MCP, which enjoys the global convergence and local superlinear convergence rate. The structure-exploiting preconditioning technique is also discussed in solving the trust-region subproblem. Numerical empirical evaluation and a comparison against other methods are reported, which shows that the method is efficient in solving MCPs.     

一类H矩阵线性互补问题的预处理二步模基矩阵分裂迭代方法

本文我们利用预处理技术推广了求解线性互补问题的二步模基矩阵分裂迭代法,并针对H-矩阵类给出了新方法的收敛性分析,得到的理论结果推广了已有的一些方法.     

On preconditioned Uzawa methods and SOR methods for saddle-point problems

This paper studies convergence analysis of a preconditioned inexact Uzawa method for nondifferentiable saddle-point problems. The SOR-Newton method and the SOR-BFGS method are special cases of this method. We relax the Bramble-Pasciak-Vassilev condition on preconditioners for convergence of the inexact Uzawa method for linear saddle-point problems. The relaxed condition is used to determine the relaxation parameters in the SOR-Newton method and the SOR-BFGS method. Furthermore, we study global convergence of the multistep inexact Uzawa method for nondifferentiable saddle-point problems.     

Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices

In this paper, the problem of inverting regular matrices with arbitrarily large condition number is treated in double precision defined by IEEE 754 floating point standard. In about 1984, Rump derived a method for inverting arbitrarily ill-conditioned matrices. The method requires the possibility to calculate a dot product in higher precision. Rump's method is of theoretical interest. Rump made it clear that inverting an arbitrarily ill-conditioned matrix in single or double precision does not produce meaningless numbers, but contains a lot of information in it. Rump's method uses such inverses as preconditioners. Numerical experiments exhibit that Rump's method converges rapidly for various matrices with large condition numbers. Why Rump's method is so efficient for inverting arbitrarily ill-conditioned matrices is a little mysterious. Thus, to prove its convergence is an interesting problem in numerical error analysis. In this article, a convergence theorem is presented for a variant of Rump's method.     

预处理对多孔硅形成过程的影响(英文)

本工作初步探讨了开路电位下对硅片进行预处理时多孔硅的形成过程 .电化学极化实验、扫描电镜和拉曼谱学的研究表明 ,预处理可以加速硅 /溶液界面上的化学或电化学反应 ,从而加快多孔硅的生长过程 ,最终导致光致发光的光谱红移 .多孔硅的厚度随预处理时间的增长而减小