预览加载中，请您耐心等待几秒...

改进的求解线性方程组的并行Arnoldi方法.docx

预览
1/2
2/2

在线预览结束，喜欢就下载吧，查找使用更方便

下载提示 文本预览

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

改进的求解线性方程组的并行Arnoldi方法 TheparallelArnoldimethodforsolvinglinearsystemshasbeenanimportantareaofresearchinthefieldofnumericallinearalgebra.Amongthevariousparallelalgorithmsusedforthispurpose,theArnoldimethodstandsoutforitsefficiencyandaccuracy.Itisaniterativemethodthatusesanorthogonalbasistoapproximatethesolutiontoalinearsystemwithalargenumberofunknowns. TheArnoldimethodisparticularlysuitableforlarge-scaleproblemsduetoitsabilitytoreducethecomputationalcostofsolvinglinearsystems.ItgeneratesasequenceofKrylovsubspaces,whichgraduallyincreaseindimensionuntiltheyspantheentirespace.Themethodishighlyeffectiveforsystemswithalargenumberofeigenvaluesthatneedtobecomputedsimultaneously.However,itsperformancedependsonthequalityoftheorthogonalbasisthatisgeneratedduringthecomputation. TheparallelArnoldimethodbuildsonthesequentialversionofthealgorithmbyexploitingtheparallelcomputingcapabilitiesofmoderncomputerarchitectures.Thisapproachallowsmultipleprocessorstoworktogethertosolvelarge-scalelinearsystemsmoreefficiently.ParallelArnoldimethodsarefrequentlyusedinscientificcomputing,wherelargelinearsystemsariseinvariouscontextssuchasscientificsimulations,machinelearning,anddataanalysis. AkeyadvantageoftheparallelArnoldimethodisitsabilitytotakeadvantageofparallelisminthecomputationofmatrix-vectorproducts.Thiscomputationisthemosttime-consumingcomponentoftheArnoldimethod.IntheparallelArnoldimethod,matrix-vectorproductsareperformedusingmultipleprocessorsconcurrently,leadingtosignificantspeed-upintheoverallalgorithm.ParallelArnoldimethodscanalsotakeadvantageofmulti-levelparallelism,wheremultipleprocessorsareusedindifferentpartsofthealgorithm. ThereareseveralvariationstotheparallelArnoldimethoddependingonthespecificproblemrequirements.Forinstance,theblockArnoldimethodcanbeusedwhenthesolutionofalargenumberoflinearsystemswiththesamecoefficientmatrixisrequired.IntheblockArnoldimethod,multiplevectorsarecomputedsimultaneously,leadingtosignificantspeed-upcomparedtothesequentialversionofthealgorithm. A