简介:Inthispaper,weproposeaparallelGauss-Seideltypeiterativemethodforsolvingthelarge-scalesystemofnonlinearalgebraicequationsAφ(x)+Bψ(x)=b,whichisanasynchronousvariantofthesynchronousparallelnonlinearGauus-SeideltypemethodgivenbyR.E.White.Withalmostthesamebutsomewhatmorerelaxedconstrainteonthemultiplesplittings,weprovetheconvergenceandestimatetheconvergencerateofthenewmethod.
简介:LetthelinearsystemAx=bwherethecoefficientmatrixA=(aij)∈Rm,nisanL-ma-trix(thatis,aij>0(?)iandaij≤0(?)i≠j),A=I-L-U,Iistheidentitymatrix,-Land-Uare,respectively,strictlylowerandstrictlyuppertriangularpartsofA.In[1]theauthorsconsideredtwopreconditionedlinearsystems?x=(?)and?x=(?)
简介:AnasynchronousparallelmultisplittingnonlinearGauss-SeideliterativemethodisestablishedfortheparticularlystructuredsystemofnonlinearequationsAφ(x)+Bφ(x)=bwithA,B∈(R^n)φ,φtR^n→R^nbeingdiagonalmappingsandb∈R^n,andtheglobalconvergenceofitisproved.
简介:在计算线性方程组时,我们有时会遇到其系数矩阵A是严格次对角占优及次正定的次对称的情形,对于这样的方程组,我们不能直接应用Jacobi、Gauss—Seidel及超松驰迭代法进行求解.在文[2]中,利用了JA是严格对角占优(占A是严格次对角占优)及JA是正定对称(当A是次正定的次对称)的性质,对方程AX=b作用J得方程JAX=Jb,对此方程我们再使用以上的方法进行求解,然而JA是对A作一条列的行变换得到的,当n是偶数时,至少要作n/2次行对换,在计算机上将A经行变换变成JA至少要进行3/2n~2次赋值,当n是奇数时,至少要进行3/2n(n-1)次赋值.并且在这个过程中还要增加n个单元的内
简介:ThepreconditionedGauss-Seideltypeiterativemethodforsolvinglinearsystems,withtheproperchoiceofthepreconditioner,ispresented.ConvergenceofthepreconditionedmethodappliedtoZ-matricesisdiscussed.Alsotheoptimalparameterispresented.NumericalresultsshowthattheproperchoiceofthepreconditionercanleadtoeffectivebythepreconditionedGauss-Seideltypeiterativemethodsforsolvinglinearsystems.
简介:TheJacobiandGauss-Seidelalgorithmsareamongthestationaryiterativemethodsforsolvinglinearsystemofequations.Theyarenowmostlyusedasprecondition-ersforthepopulariterativesolvers.Inthispaperageneralizationofthesemethodsareproposedandtheirconvergencepropertiesarestudied.Somenumericalexperimentsaregiventoshowtheefficiencyofthenewmethods.
简介:文章利用求解线性方程组的Gauss-Seidel迭代法推导出其"反方法",正反两种方法相匹配生成预报-校正系统,给出了它们收敛的条件,并运用这三种不同的公式求解实例,根据其结果,说明这些公式的优缺点。
简介:三坐标测量仪在管类产品的加工验证中高频使用。在管形坐标的测量中,由于测量坐标系与设计测量系很难保持一致,通常需要将测量坐标在CAD软件中通过旋转、平移等操作与设计坐标进行吻合调整。但此操作依靠人眼进行吻合度判断,对比精度会大大降低,使三坐标测量仪的高精度得不到真正的发挥。本文在建立空间管形自由状态方程和两端约束管形方程的基础上,建立两种模型下的测量坐标管形与设计管形之间的最佳逼近目标方程,采用Gauss-Newton法对测量管形与设计管形进行最佳逼近求解,减少人为操作误差,提高测量精度。
简介:ForasimpleundirectedgraphG,denotebyA(G)the(0,1)-adjacencymatrixofG.LetthematrixS(G)=J-I-2A(G)beitsSeidelmatrix,andletSG(λ)=det(λI-S(G))beitsSeidelcharacteristicpolynomial,whereIisanidentitymatrixandJisasquarematrixallofwhoseentriesareequalto1.IfalleigenvaluesofSG(λ)areintegral,thenthegraphGiscalledS-integral.Inthispaper,ourmaingoalistoinvestigatetheeigenvaluesofSG(λ)forthecompletemultipartitegraphsG=Kn1,n2,...,nt.AnecessaryandsufficientconditionforthecompletetripartitegraphsKm,n,tandthecompletemultipartitegraphsKm,...,ms,n,...,nttobeS-integralisgiven,respectively.
简介:TheauthorobtainsaWeierstrassrepresentationforsurfaceswithprescribednormalGaussmapandGausscurvatureinH3.AdifferentialequationaboutthehyperbolicGaussmapisalsoobtained,whichcharacterizestherelationamongthehyperbolicGaussmap,thenormalGaussmapandGausscurvature.TheauthordiscussestheharmonicityofthenormalGaussmapandthehyperbolicGaussmapfromsurfacewithconstantGausscurvatureinH3toS2withcertainalteredconformalmetric.Finally,theauthorconsidersthesurfacewhosenormalGaussmapisconformalandderivesacompletelynonlineardifferentialequationofsecondorderwhichgraphmustsatisfy.
简介:Inthispaper,ageneralalgorithmforthecomputationoftheFouriercoefficientsof2π-periodic(continuous)functionsisdevelopedbasedonDirichletcharacters,GausssumsandthegeneralizedM¨obiustransform.ItpermitsthedirectextractionoftheFouriercosineandsinecoefficients.Threespecialcasesofouralgorithmarepresented.AVLSIarchitectureispresentedandtheerrorestimatesaregiven.
简介:提出一种改进的并行比特翻转算法.为了加快校验节点和变量节点之间的信息传递速率,算法中的比特翻转及校验和更新2个步骤采用并行化处理.仿真结果表明,改进后的算法相对于原有的并行比特翻转算法在误帧率性能上能够取得0.1~0.3dB的增益.同时,改进算法在译码吞吐率的性能上也有所改善.此外,还讨论了翻转门限的选择方法,这些门限决定了每次迭代中哪些比特需要被翻转.通过选择合适的翻转门限,可使错误的比特尽量多地被翻转,并避免翻转正确的比特.该改进算法比较适用于对具有准循环结构的LDPC码进行译码.
简介:Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.