Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix–vector products per iteration without accessing A^T. We apply this algorithm to obtain a transpose-free version of the Quasi-minimal residual method of Freund and Nachtigal [15] (without look-ahead), which requires three matrix–vector products per iteration. We also present a related transpose-free version of the bi-conjugate gradients algorithm. This revised version was published online in June 2006 with corrections to the Cover Date.     

Continuation of Invariant Subspaces via the Recursive Projection Method

The Recursive Projection Method is a technique for continuation of both the steady states and the dominant invariant subspaces. In this paper a modified version of the RPM called projected RPM is proposed. The modification underlines the stabilization effect. In order to improve the poor update of the unstable invariant subspace we have applied subspace iterations preconditioned by Cayley transform. A statement concerning the local convergence of the resulting method is proved. Results of numerical tests are presented.     

一类混杂动态系统的能控性（I）——基本结果

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成，第I部分首先，提出含时滞的线性切换系统的数学模型，并介绍切换系统的基本概念——切换序列．其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理．然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用．这些概念和引理都将作为以后展开能控性分析所必需的研究工具．     

Noninterpolatory Hermite subdivision schemes

Bivariate interpolatory Hermite subdivision schemes have recently been applied to build free-form subdivision surfaces. It is well known to geometric modelling practitioners that interpolatory schemes typically lead to ``unfair" surfaces--surfaces with unwanted wiggles or undulations--and noninterpolatory (a.k.a. approximating in the CAGD community) schemes are much preferred in geometric modelling applications. In this article, we introduce, analyze and construct noninterpolatory Hermite subdivision schemes, a class of vector subdivision schemes which can be applied to iteratively refine Hermite data in a not necessarily interpolatory fashion. We also study symmetry properties of such subdivision schemes which are crucial for application in free-form subdivision surfaces.

A key step in our mathematical analysis of Hermite type subdivision schemes is that we make use of the strong convergence theory of refinement equations to convert a prescribed geometric condition on the subdivision scheme--namely, the subdivision scheme is of Hermite type--to an algebraic condition on the subdivision mask. The latter algebraic condition can then be used in a computational framework to construct specific schemes.

     

Multipliers of weighted spaces and reflexivity property

We prove for some translation-invariant weighted spaces the following characterization: is a multiplier of if and only if leaves invariant every translation-invariant subspace of . This result is equivalent with the reflexivity of the multiplier algebra of .

     

周期量级激光脉冲在不同密度的原子介质中传播行为的比较(英文)

利用不含慢变包络近似和旋波近似的全波Maxwell-Bloch方程组的数值解,研究了周期量级超短激光脉冲在Ladder型三能级原子介质中的传播行为并与在相应的稀疏介质中的情况进行了比较.我们发现,在传播过程中,超短脉冲在稠密介质中的时间演化规律与在稀疏介质中明显不同,而且这种差别将随初始脉冲面积的增大而加大.当初始脉冲面积较小时,在传播过程中,脉冲形状在稀疏介质中只有小的改变而在稠密介质中却有显著的变化.当初始脉冲面积足够大时,在稠密介质中在不同的传播距离处脉冲分裂为不同数量和形状的亚脉冲;在稀疏介质中脉冲形状在传播过程中仍然只有小的改变。产生以上差别的原因在于稠密原子介质中近偶极-偶极(NDD)相互作用导致的局域场修正(LFC)及比稀疏原子介质更强的极化电场的影响.其中,更强的极化电场的影响起着主要的作用,但局域场修正的作用也不能忽略,而极化电场的增强是由于原子密度的增加.     

Rank-one commutators on invariant subspaces of the Hardy space on the bidisk

We discuss on invariant subspaces of H²(Γ²) on which .     

An adaptive truncation criterion,for linesearch-based truncated Newton methods in large scale nonconvex optimization

Starting from the paper by Nash and Sofer (1990), we propose a heuristic adaptive truncation criterion for the inner iterations within linesearch-based truncated Newton methods. Our aim is to possibly avoid “over-solving” of the Newton equation, based on a comparison between the predicted reduction of the objective function and the actual reduction obtained. A numerical experience on unconstrained optimization problems highlights a satisfactory effectiveness and robustness of the adaptive criterion proposed, when a residual-based truncation criterion is selected.