广义异步并行多分裂松弛算法

在本文中，我们设计了求解大型线性代数方程组的适用于ＭＩＭＤ系统的异步并行多分裂松弛算法的一般模型，并在系数矩阵是Ｈ－矩阵的条件下，建立了该一般模型的收敛性理论。     

异步并行矩阵多分裂块松弛迭代算法

1 引言 众所周知,许多微分方程经过差分或有限元离散,即可归结为线性代数方程组 Ax=b,A∈L(R~n)非奇异,x,b∈R~n.(1.1)缘于原问题的物理特性,系数矩阵A∈L(R~n)通常是大型稀疏的,并且具有规则的分块结构。鉴此,文[1]基于矩阵多重分裂的概念,并运用线性迭代法的松弛加速技巧,提出了求解这类大型稀疏分块线性代数方程组的并行矩阵多分裂块松弛迭代算法,并在适当的条件下建立了算法的收敛理论。对于SIMD多处理机系统,这类算法是颇为适用和行之有效的。     

ON THE CONVERGENCE OF ASYNCHRONOUS NESTED MATRIX MULTISPLITTING METHODS FOR LINEAR SYSTEMS

1.IntroductionTherehasbeenalotofliterature(see[1]--[61and[12])ontheparalleliterativemethodsforthelarge--scalesystemoflinearequationsinthesenseofmatrixmultisplittingsincethepioneeringworkofO'LearyandWhite(see[l])waspublishedin1985.Oneofthemostrecentre...     

EXPERIMENTAL STUDY OF THE ASYNCHRONOUS MULTISPLITTING RELAXATION METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEMS

We study the numerical behaviours of the relaxed asynchronous multisplitting methods for the linear complementarity problems by solving some typical problems from practical applications on a real multiprocessor system. Numerical results show that the parallel multisplitting relaxation methods always perform much better than the corresponding sequential alternatives, and that the asynchronous multisplitting relaxation methods often outperform their corresponding synchronous counterparts. Moreover, the two-sweep relaxed multisplitting methods have better convergence properties than their corresponding one-sweep relaxed ones in the sense that they have larger convergence domains and faster convergence speeds. Hence, the asynchronous multisplitting unsymmetric relaxation iterations should be the methods of choice for solving the large sparse linear complementarity problems in the parallel computing environments.     

A CLASS OF ASYNCHRONOUS PARALLEL MULTISPLITTING RELAXATION METHODS FOR LARGE SPARSE LINEAR COMPLEMENTARITY PROBLEMS

Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties,are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.     

解椭圆变分不等式问题的区域分裂与异步并行算法

本文给出了两类解椭圆变分不等式问题的区域分裂异步并行算法，证明了解在Ｈ＾１－模意义下的收敛性，并给出离散格式及算例。     

WAVEFORM RELAXATION METHODS AND ACCURACY INCREASE

ＷＡＶＥＦＯＲＭ　ＲＥＬＡＸＡＴＩＯＮ　ＭＥＴＨＯＤＳ　ＡＮＤ　ＡＣＣＵＲＡＣＹ　ＩＮＣＲＥＡＳＥＷＡＶＥＦＯＲＭＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳＡＮＤＡＣＣＵＲＡＣＹＩＮＣＲＥＡＳＥ￥ＳｏｎｇＹｏｎｇｚｈｏｎｇ（ＮａｎｊｉｎｇＮｏｒｍａｌＵｎｉｖ...     

COMBINING METHODS OF PEST CONTROL: COMPLEMENTARITY OF METHODS AND A GUIDING PRINCIPLE

Four sets of models are examined which represent various pairwise combinations of several methods of pest control. These methods involve the release of sterile male pests, the inundative release of parasitoids, insecticide application, pheromone trapping and food-baited trapping with either insecticides or sterilants. It was observed that two pest control methods will combine synergistically, and thus be complimentary, if their optimal action is at different pest densities and varies differently with pest density. The synergism thus generated by differing dependence on density, can however, be obscured if the two control methods interfere with each other in some other way, as occurs for example with the use of both insecticides and inundative release of parasitoids.     

ASYNCHRONOUS MULTISPLITTING NONLINEAR GAUSS-SEIDEL TYPE METHOD

ＡＳＹＮＣＨＲＯＮＯＵＳＭＵＬＴＩＳＰＬＩＴＴＩＮＧＮＯＮＬＩＮＥＡＲＧＡＵＳＳ－ＳＥＩＤＥＬＴＹＰＥＭＥＴＨＯＤ￥ＢＡＩＺＨＯＮＧＺＨＩＡＮＤＷＡＮＧＤＥＲＥＮＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｐｒｏｐｏｓｅａｐａｒａｌｌｅｌＧａｕｓｓ...     

PROBLEMS AND METHODS IN MATRIX VALUED RATIONAL INTERPOLATION

A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit theory and digital filter design can also be re-duced to the solution of matrix rational interpolation problems[1—4].By means of thereachability and the observability indices of defined pairs of matrices,Antoulas,Ball,Kang and Willems solved the minimal matrix rational interpolation problem in[1].On the     

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE

In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an L-matrix.     

QUADRATIC INVARIANTS AND SYMPLECTIC STRUCTURE OF GENERAL LINEAR METHODS

1. IntroductionInvestigating whether a numerical method inherits some dynamical properties possessed bythe differential equation systems being integrated is an important field of numerical analysisand has received much attention in recent years See the review articlesof Sanz-Serna[9] and Section 11.16 of Hairer et. al.[2] for more detail concerning the symplectic methods. Most of the work on canonical iotegrators has dealt with one-step formulaesuch as Runge-Kutta methods and Runge'methods …     

MODELS OF ASYNCHRONOUS MRALLEL NONLINEAR MULTISPLITTING RELAXED ITERATIONS

1.IntroductionConsiderthelargescalesystemofnonlinearequationsF(x)=O,F:DcR"-R".(1'1)Givena(cr5n5aninteger)nonemptysubsetsJi(i=1,2,'',cr)oftheset{1,2,''3n}withwhereJ1,J2,'',JamayoverlaPamongthem.Fori=1,2,'')a,weassumethatb)E=diag(e1`),e;`),'-',e2))EL(R")satisfiesThen,thecollectionofpairs(f('),E)(i=1,2,'',a)iscalledanonlinearmultisplittingofthemaPpingF:DCR"-R".Nowadays,therehavebeenalot0fmoredeepenedresearchresultsonb0ththepaxallelmethods,designedbymakinguseofthisconceptfors0lvingt…     

MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS

In this paper we propose the well-known Fourier method on some non-tensor productdomains in R~d, inclding simplex and so-called super-simplex which consists of (d 1)!simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallelhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended mostof concepts and results of the traditional Fourier methods on multivariate cases, such asFourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT)and related fast algorithms over a simplex. The relationship between the basic orthogonalsystem and eigen-functions of a Laplacian-like operator over these domains is explored.     

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

1　ＩｎｔｒｏｄｕｃｔｉｏｎＷｅｃｏｎｓｉｄｅｒｌｉｎｅａｒｓｙｓｔｅｍｓｏｆｔｈｅｆｏｒｍＡｘ=ｂ,(1 )ｗｈｅｒｅＡ∈ＣＮ×Ｎｉｓｎｏｎｓｉｎｇｕｌａｒａｎｄｐｏｓｓｉｂｌｙｎｏｎ Ｈｅｒｍｉｔｉａｎ .Ａｍａｊｏｒｃｌａｓｓｏｆｍｅｔｈｏｄｓｆｏｒｓｏｌｖｉｎｇ (1 )ｉｓｔｈｅｃｌａｓｓｏｆＫｒｙｌｏｖｓｕｂｓｐａｃｅｍｅｔｈｏｄｓ (ｓｅｅ[6] ,[1 3]ｆｏｒｏｖｅｒｖｉｅｗｓｏｆｓｕｃｈｍｅｔｈｏｄｓ) ,ｄｅｆｉｎｅｄｂｙｔｈｅｐｒｏｐｅｒｔｉｅｓｘｍ ∈ｘ0 +Ｋｍ(ｒ0 ,Ａ) ;(2 )ｒｍ ⊥Ｌｍ, (3)ｗｈｅ…     

RELAXED ASYNCHRONOUS ITERATIONS FOR THE LINEAR COMPLEMENTARITY PROBLEM

1. IntroductionConsider the large sparse Linear Complementarity Problem (LCP):where .1I = (mkj) 6 L(R) is a gitren real matrix and q = (qk) E R a given real vector. Thisproblem arises in many areas of scientific computing. FOr example, it arises from problemsin (linear and) contrex quadratic programming, the prob1em of finding a Nash equilibriumpoint of a bimatrix game (e.g., Cottle and Dantzig[5] and Lemke[13]), a11d also a number of freeboundary problems of fluid mechanics (e.g., Cr…     

一类具有L稳定和B稳定的Runge—Kutta方法

在求解刚性常微分方程的数值解法中,为了使获得的结果稳定,人们往往使用具有L稳定和B稳定的数值方法,本文利用W－变换构造了一类具有L稳定和B[稳定的Runge-Kutta(RK)方法。     

PARALLEL SEMI ITERATIVE AND ITERATIVE METHODS FOR SINGULAR M-MATRICES

This paper praidrs a theurvtheal hasts for establishing the congergente of paraled interative and itratiee techaigues,for computing nmtrfied solution of Ar three A is a singal M-matrix,These results do not assuine A to irreducihle,A concrete relaxed parallet multixpla ting algorithin culled the parallel multispliting AOR algarithm is showed Findly,numericales amples are givep,arhleh show effertielve of parallel iterurise methods for singalar case