The Nonlinear Lopsided HSS-Like Modulus-Based Matrix Splitting Iteration Method for Linear Complementarity Problems with Positive-Definite Matrices

In this paper,by means of constructing the linear complementarity problems into the corresponding absolute value equation,we raise an iteration method,called as the nonlinear lopsided HSS-like modulus-based matrix splitting iteration method,for solving the linear complementarity problems whose coefficient matrix in R^(n×n)is large sparse and positive definite.From the convergence analysis,it is appreciable to see that the proposed method will converge to its accurate solution under appropriate conditions.Numerical examples demonstrate that the presented method precede to other methods in practical implementation.

Modulus-Based Matrix Splitting Iteration Methods for a Class of Stochastic Linear Complementarity Problem

For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.

On the Convergence of Two-Step Modulus-Based Matrix Splitting Iteration Methods for a Restricted Class of Nonlinear Complementarity Problems with H_(+) -Matrices

We propose the two-step modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problems.The corresponding convergence the-ory is established when the system matrix is an H_(+)-matrix.Theoretical analysis gives the choice of parameter matrix involved based on the H-compatible splitting of the sys-tem matrix.Moreover,in actual implementation,the choices of iterative parameters for two-step modulus-based accelerated overrelaxation methods are studied.Numeri-cal experiments show that the method is efficient and further verify the convergence theorems.

Comparative analysis of energy-level splitting of Pr^(3+) doped in LiYF_4 and LiBiF_4 crystals:a complete energy matrix calculation

Based on the combination of Racah＇s group-theoretical consideration with Slater＇s wavefunction, a 91 ×91 complete energy matrix is established in tetragonal ligand field D2d for Pr3＋ ion. Thus, the Stark energy-levels of Pr3＋ ions doped separately in LiYF4 and LiBiF4 crystals are calculated, and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions. Besides, the influence of Pr3＋ on energy-level splitting is investigated, and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities. We see that the energy splitting patterns are similar and the crystal field interaction of LiYF4：Pr3＋ is stronger than that of LiBiF4：Pr3＋.

THE SPECTRAL PROPERTIES OF THE ITERATION MATRIX OF REGULAR SPLITTINGS FOR AN M-MATRIX

Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.

SIGN MATRIX, REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS, PARTI

In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.

Preconditioned Iterative Method for Regular Splitting

Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitting. The purpose of this paper is to show that the preconditioned iterative method yields a new splitting satisfying the regular or weak regular splitting. And new combination preconditioners are proposed. In order to denote the validity of the comparison theorem, some numerical examples are shown.

BANDED M-MATRIX SPLITTING PRECONDITIONER FOR RIESZ SPACE FRACTIONAL REACTION-DISPERSION EQUATION

Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference scheme.However,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently small.To overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient matrix.Some properties of this preconditioner together with its preconditioning effect are discussed.Finally,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.

TWO-STEP MODULUS-BASED SYNCHRONOUS MULTISPLITTING ITERATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.

Analysis of Adiabatic Shearing Failure Mechanism for Aluminum Matrix Composites Based on Experimental and Numerical Simulation

Adiabatic shear behavior and the corresponding mechanism of TiB2/Al composites were researched by split Hopkinson pressure bar （SHPB）.Results show that the flow stresses of the TiB2/Al composites exhibit softening tendency with the increasing of strain rates. All the composites fail in splitting and cutting with a 45 degree, and the phase transformed bands of molten aluminum are found on the adiabatic shear layers. The deformation behavior and shear localization of the TiB2/Al composites specimens were simulated by finite element code MSC.Marc. The Johnson-Cook model was used to describe the thermo-viscoplastic response of the specimen material. There was unanimous between the numerical result and the experimental result on the location of the adiabatic shear band. From the numerical simulation and experiment, it was concluded that the instantaneous failure of the composite was ascribed due to the local low strength area where the formation of adiabatic shear band was, and the stress condition had significant effect on the initiation and propagation of adiabatic shear band （ASB）.

A New Approximation to the Linear Matrix Equation AX = B by Modification of He’s Homotopy Perturbation Method

It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.

Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data

The method of recovering a low-rank matrix with an unknown fraction whose entries are arbitrarily corrupted is known as the robust principal component analysis （RPCA）. This RPCA problem, under some conditions, can be exactly solved via convex optimization by minimizing a combination of the nuclear norm and the 11 norm. In this paper, an algorithm based on the Douglas-Rachford splitting method is proposed for solving the RPCA problem. First, the convex optimization problem is solved by canceling the constraint of the variables, and ~hen the proximity operators of the objective function are computed alternately. The new algorithm can exactly recover the low-rank and sparse components simultaneously, and it is proved to be convergent. Numerical simulations demonstrate the practical utility of the proposed algorithm.

宫颈癌调强计划Portal Dosimetry剂量验证中拼接野的应用分析

目的提出一种生成Portal Dosimetry(以下简称PD)分野的拼接野(以下简称PD拼接野)方法,并对宫颈癌计划的PD拼接野进行分析研究。方法选取20例宫颈癌患者的七野调强治疗计划进行研究,治疗计划中每个大野分成1对分野。首先制作仅含分野的PD剂量验证计划,然后使用直线加速器出束执行。通过矩阵拼接和矩阵叠加,分别得到每对PD分野对应的PD拼接野和PD大野。使用PD软件模块,得到PD拼接野和PD大野的伽玛通过率,分别记为Gp和Gd。使用Gm表示每对PD分野的平均伽玛通过率值。对Gp、Gd和Gm进行统计分析和比较研究。结果所有140个射野的Gp、Gd和Gm的值分别为98.78%±0.70%、97.34%±1.25%和98.87%±0.51%。两两比较结果显示,Gp和Gd差异具有统计学意义(P<0.05);Gp和Gm的数据差异较小。对每个PD验证计划,计算所有同一类射野对应的计划验证通过率(Gplan)。对Gplan数据进行统计分析显示,PD拼接野和PD大野差异具有统计学意义(P<0.05),PD拼接野和PD分野的数据差异较小。结论本文提出的PD拼接野概念为评价PD剂量验证结果提供了有益的参考信息。

关于矩阵三种典型分裂及应用

本文讨论了矩阵的Cartesian分裂、Jordan分裂、核心-幂零分裂的存在性与唯一性;将Jordan块的主要特性推广到一般矩阵;获得了一般矩阵具有的性质.以上关于矩阵分裂结果充实并深化了矩阵分裂的已有结果,并有助于提高学生学习高等代数及矩阵分析理论与应用的能力,以便为利用矩阵理论解决实际问题奠定了基础.

多元统计分析中一类矩阵迹函数极小化问题的分裂迭代法

研究了来源于多元统计分析中的一类含列正交约束的矩阵迹函数极小化模型,该模型的特殊形式广泛应用于多维标度分析中DEDICOM模型和正交INDSCAL模型最小二乘拟合等问题中。结合变量分裂构造了几类经典的基于分裂的不可行迭代算法求解该约束迹函数极小化模型,并给出算法外层迭代框架和内层子问题的具体求解方案。数值实验验证了算法的有效性。

碳基跨尺度纤维增强混凝土劈拉性能及微观界面研究

为改善碳纤维增强混凝土(CFRC)内部的纤维/基体(F/M)界面性能,提出利用碳纳米管-碳纤维跨尺度增强体(CNTs-CF)对F/M微观界面进行改性的技术方法。设计制作了CNTs-CF体积分数分别为0%、0.1%、0.2%、0.3%和0.4%的跨尺度纤维增强混凝土(CCFRC)试件,进而对其开展了劈裂抗拉实验,并与CFRC进行对比分析。结果表明,在相同的纤维掺量情况下,CCFRC能够在劈拉破坏失效时维持更好的整体性,而且CCFRC的劈裂抗拉强度明显高于CFRC。CCFRC的劈裂抗拉强度随纤维掺量的增加呈先逐渐升高后略有下降的变化趋势,当CNTs-CF的体积分数为0.3%时达到最大值,较之普通混凝土(PC)和CFRC,增长幅度分别达37.67%和13.21%。CNTs-CF兼具碳纤维和碳纳米管的优良特性,能够充分发挥跨尺度协同改性效应,强化F/M界面。CCFRC在工程结构抗力提升,以及基础设施电磁防护领域具有广阔的应用发展前景。

TOPIC SPLITTING： A HIERARCHICAL TOPIC MODEL BASED ON NON-NEGATIVE MATRIX FACTORIZATION

Hierarchical topic model has been widely applied in many real applications, because it can build a hierarchy on topics with guaranteeing of topics＇ quality. Most of traditional methods build a hierarchy by adopting low-level topics as new features to construct high-level ones, which will often cause semantic confusion between low-level topics and high-level ones. To address the above problem, we propose a novel topic model named hierarchical sparse NMF with orthogonal constraint （HSOC）, which is based on non-negative matrix factorization and builds topic hierarchy via splitting super-topics into sub-topics. In HSOC, we introduce global independence, local independence and information consistency to constraint the split topics. Extensive experimental results on real-world corpora show that the purposed model achieves comparable performance on topic quality and better performance on semantic feature representation of documents compared with baseline methods.

Another SSOR Iteration Method

Kellogg gave a version of the Peaceman-Radford method. In this paper, we introduce a SSOR iteration method which uses Kellogg’s method. The new algorithm has some advantages over the traditional SSOR algorithm. A Cyclic Reduction algorithm is introduced via a decoupling in Kellogg’s method.

求解PageRank向量的一种松弛多步分裂迭代方法

基于求解PageRank向量的内外迭代格式,引入一个松弛因子得到一种松弛内外迭代方法。结合已有的多步分裂迭代框架,引入两个不同的松弛因子,提出了求解PageRank向量的松弛多步分裂迭代方法并分析了算法的收敛性。更进一步地,利用松弛内外迭代格式构造了加速投影子空间方法的预处理矩阵,理论分析相关谱分布情况,并给出了松弛多步分裂迭代方法及预处理矩阵中参数的选取准则。几个数值例子验证了松弛多步分裂迭代方法和预处理矩阵的有效性,通过选取合适的松弛因子,与多步分裂迭代方法相比具有更高的运算效率。

基于分离源的高增益矩阵变换器特性分析

针对矩阵变换器(MC)存在的电压传输比限制以及现有升压型MC结构元件多、调制复杂的问题,提出了一种新型的分离源型矩阵变换器(SS-MC)。该结构采用电感、电容和3个二极管替代了双级MC中间的直流链路部件,从而构成分离源升压网络,避免了配置额外的直通占空比。对SS-MC的拓扑结构和分离源网络升压的工作原理进行了分析,阐述了其采用的空间矢量脉宽调制(SVPWM)策略,并针对SVPWM的缺点提出了基于充电预测的模型预测控制(CPB-MPC)策略。仿真和实验结果表明:所提出的SS-MC结构使用常规的SVPWM即可达到较高的电压传输比,但无源元件会存在较大的纹波;使用CPB-MPC策略可以有效抑制纹波,提高MC的输出电能质量。