PARALLEL NONLINEAR MULTISPLITTING RELAXATION METHODS

ＰＡＲＡＬＬＥＬＮＯＮＬＩＮＥＡＲＭＵＬＴＩＳＰＬＩＴＴＩＮＧＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳＷＡＮＧＤＥＲＥＮＡＮＤＢＡＩＺＨＯＮＧＺＨＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎ...     

A CLASS OF GENERALIZED MULTISPLITTING RELAXATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high-speed multiprocessor systems is set up. This class of methods not only includes all the existing relaxation methods for the linear complementarity problems ,but also yields a lot of novel ones in the sense of multisplittlng. We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H-metrix with positive diagonal elements.     

ON THE CONVERGENCE DOMAIN OF THEMATRIX MULTISPLITTING RELAXATION METHODS FOR LINEAR SYSTEMS

The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473-486) is further investigated.The investigations show that these relaxation methods really have considerably larger convergence domains.     

WAVEFORM RELAXATION METHODS AND ACCURACY INCREASE

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

ON THE CONVERGENCE OF THE RELAXATION METHODS FOR POSITIVE DEFINITE LINEAR SYSTEMS

1.IntroductionTheclassicaliterativemethods,suchastheJacobimethod,theGauss-SeidelmethodandtheSORmethod,aswellastheirsymmetrizedvariants,playanimportantroleforsolvingthelargesparsesystemoflinearequationsInaccordancewiththebasicextrapolationprincipleofthelineariterativemethod,Hadjidimos[1]furtherproposedaclassofacceleratedoverrelaxation(AOR)methodforsolyingthelinearsystem(1.1)in1978.Thismethodincludestwoarbitraryparameters,andtheirsuitablechoicesnotonlycannaturallyrecovertheJacobi,theGauss-S…     

GENERALIZED CONIC CURVES AND THEIR APPLICATIONS IN CURVE APPROXIMAION

The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curves i including parabolas, hyperbolas and ellipses;(ii) generalized monomial curves, including curves of the form x=yr,.r R.r=0,1, in the x-y Cartesian coordinate system;(iii) exponential spiral curves of the form p=Apolar coordinate system.This type of curves has many important properties such as convexity , approximation property, effective numerical computation property and the subdivision property etc. Applications of these curves in both interpolation and approximations using piecewise generalized conic segment are also developed. It is shown that these generalized conic splines are very similar to the cubic polynomial splines and the best error of approximation is or at least in general provided appropriate procedures are used. Finally some numerical examples of interpolation and appro     

CONVERGENCE OF INEXACT CONIC NEWTON METHODS

A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals.     

BOOTSTRAPPING GENERALIZED U－PROCESSES AND V－PROCESSES AND THEIR APPLICATIONS IN PROJECTION PURSUIT

ＢＯＯＴＳＴＲＡＰＰＩＮＧＧＥＮＥＲＡＬＩＺＥＤＵ－ＰＲＯＣＥＳＳＥＳＡＮＤＶ－ＰＲＯＣＥＳＳＥＳＡＮＤＴＨＥＩＲＡＰＰＬＩＣＡＴＩＯＮＳＩＮＰＲＯＪＥＣＴＩＯＮＰＵＲＳＵＩＴ￥ＺＨＡＮＧＤＩＸＩＮ（张涤新）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉ...     

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。     

A CLASS OF ASYNCHRONOUS MATRIX MULTI-SPLITTING MULTI-PARAMETER RELAXATION ITERATIONS

1.IntroductionMultisplittingmethodsforgettingthesolutionoflargesparsesystemoflinearequationsAx=b,A=(and)6L(Rn)nonsingular,x=(x.),b=(b.)eR"(1.1)areefficientparalleliterativemethodswhicharebasedonseveralsplittingsofthecoefficientmatrixAEL(R").Following[11th…     

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。     

矩阵多分裂迭代法的收敛条件

本文给出了求解非奇异线性方程组的矩阵多分裂并行迭代法的一些新的收敛结果.当系数矩阵单调和多分裂序列为弱正则分裂时,得到了几个与已有的收敛准则等价的条件,并且证明了异步迭代法在较弱条件下的收敛性.对于同步迭代,给出了与异步迭代不同且较为宽松的收敛条件.     

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...     

ON MONOTONE CONVERGENCE OF NONLINEARMULTISPLITTING RELAXATION METHODS

ＯＮＭＯＮＯＴＯＮＥＣＯＮＶＥＲＧＥＮＣＥＯＦＮＯＮＬＩＮＥＡＲＭＵＬＴＩＳＰＬＩＴＴＩＮＧＲＥＬＡＸＡＴＩＯＮＭＥＴＨＯＤＳ￥ＷＡＮＧＤＥＲＥＮ;ＢＡＩＺＨＯＮＧＺＨＩ（ＤｅｐａｚａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｈｓｌｌｇｈａｉＵｎｉｖｅ...     

ON THE CONVERGENCE OF WAVEFORM RELAXATION METHODS FOR LINEAR INITIAL VALUE PROBLEMS

We study a class of blockwise waveform relaxation methods,and investigate its con-vergence properties in both asymptotic and monotone senses.In addition,the monotoneconvergence rates between different pointwise/blockwise waveform relaxation methods re-sulted from different matrix splittings,and those between the pointwise and blockwisewaveform relaxation methods are discussed in depth.     

A NEW GENERALIZED ASYNCHRONOUS PARALLEL MULTISPLITTING ITERATION METHOD

1.IntroductionTosolvelargesparsesystemsoflinearandnonlinearequationsonthemultiprocessorsystems,manyauthorspresentedandstudiedvariousparalleliterativemethodsinthesenseofmultisplittinginrecentyears.FOrdetailsonecanreferto[1]-[9]andreferencestherein.Amo...     

二阶锥线性互补问题的广义模系矩阵分裂迭代算法

通过将二阶锥线性互补问题转化为等价的不动点方程,介绍了一种广义模系矩阵分裂迭代算法,并研究了该算法的收敛性.进一步,数值结果表明广义模系矩阵分裂迭代算法能够有效地求解二阶锥线性互补问题.