雨课堂学堂在线学堂云《Scientific Computing and Mathematical Modeling( 中南)》单元测试考核答案

注：不含主观题第1题单选题(1分)Theapproximatevalueof

0.048657168with5significantdigitsis________A0.04865B0.048657C0.0486D0.0486571第2题单选题(1分)Lettheabsoluteerrorofdatax1,x2

be0.025and0.006respectively,thentheabsoluteerroroftheproductofx1x2

is________.A0.025x1x2B0.025C0.025x2+0.006x1D0.031(x1+x2)第3题单选题(1分)Suppose

thattherelativeerrorofx

is2%,

thentherelativeerrorofxn

is_________.An×2%B2%Cn2%D(2%)n第4题单选题(1分)Iftheexactvalueis100,theabsoluteandrelativeerrorsoftheapproximatevalue99.9arerespectively

__________.A0.1,0.01B0.1,0.001C0.01,0.001D0.001,0.1第5题单选题(1分)Supposethattheabsoluteerrorlimitsoftheobserveddatax1,x2,x3

are

all0.001，thentheabsoluteerrorlimitsofx1x2x3

is______.

A0.001B0.003

C0.002D0.004第6题单选题(1分)Roundingerroristheerrorcausedby___________.AtakingonlyafinitenumberofdigitsBtheexactvalueofthemodelandtheexactvalueobtainedbynumericalmethodCobservationandmeasurementDmathematicalmodelexactvalueandactualvalue第7题判断题(1分)Theexactsolutionistheanalyticalsolution.第8题判断题(1分)Analgorithmissaidtobenumericallystable,ifthereisanerrorintheinputdataandtheroundingerrordoesnotincreaseduringthecalculation,

Otherwise,itiscalledunstable.第9题判断题(1分)Simplifyingthestepshelpsreducethenumberofoperations.第10题判断题(1分)Truncationerrorisalsocalledmethoderror.Chapter2_Unittest第1题单选题(1分)Theonlyconditionfortheexistenceofann-degreeinterpolationpolynomialisthat

.AithasnnodesBithasn+1nodesC

thereareninterpolationconditionsDn+1nodesaredistinctfromeachother第2题单选题(1分)ThefunctionvalueofLagrangeinterpolationbasisfunction

l1(x)

atnode

x0isl1(x0)=___。A1B-1C0D2第3题单选题(1分)Theinterpolationpolynomial_________withthenumberofnodesincreasing.AincreasesBdecreasesCdoesnotincreaseDmayoscillateviolentlyatsomepoints第4题单选题(1分)FortheselectionofNewtonforwardinterpolationformulaandNewtonbackwardinterpolationformula,

Whenthepointx

tobecalculatedisnearthestartingpointx0,theNewton______

interpolationformulashouldbeused,

Whenthepointx

tobecalculatedisnearthestartingpointxn,theNewton______

interpolationformulashouldbeused.Aforward，forwardBforward，backwardCbackward，forwardDbackward，backward第5题单选题(1分)Piecewiselow-orderinterpolationovercomestheproblemthathigh-orderinterpolationpolynomialsmayoscillate,However,piecewiselow-orderinterpolationfunctioncannotguarantee

_________inthewholeinterpolationinterval?AcontinuityBfirstderivativeexistsCfirst-orderderivativecontinuousDSecondderivativeexists第6题单选题(1分)Thefittingeffectoffittingfunctionisusuallyestimatedwithout________。AthesumofdeviationBaveragedeviationofthesumoftheabsolutevalueCthesumofsquaresofdeviationsDmeansquareerror(mse)第7题单选题(1分)Lagrangeinterpolationcalculation：giveny=x,x0=4,x1=9，theapproximatevalueof6

is______

byLagrangelinearinterpolation.

A2.1B2.2C2.3D2.4第8题单选题(1分)Givenf(-1)=2,f(1)=1,f(2)=1，thentheLagrangeinterpolationpolynomialoff(x)

is______.AL(x)=(x−1)(x−2)(−1−1)(−1−2)+(x+1)(x−2)(1+1)(1−2)+(x+1)(x−1)(2+1)(2−1)BL(x)=(x−1)(x−2)(−1−1)(−1−2)×2+(x+1)(x−2)(1+1)(1−2)+(x+1)(x−1)(2+1)(2−1)CL(x)=(x+1)(x−2)(−1+1)(−1−2)×2+(x+1)(x−2)(1+1)(1−2)+(x+1)(x−1)(2+1)(2−1)DL(x)=(x−1)(x−2)(−1−1)(−1−2)×2+(x+1)(x+2)(1+1)(1+2)+(x+1)(x−1)(2+1)(2−1)第9题单选题(1分)Givenvalueoffunctionf(0)=2,f(1)=3,f(2)=5,f(3)=4,f(4)=1，thenthesecondorderforwarddifferenceofthefunctionat

x=2

is

.A-1B0C1D2第10题单选题(1分)Givenvalueoffunction

f(0)=2,f(1)=3,f(2)=5,f(3)=4,f(4)=1，thenthesecondorderbackwarddifferenceofthefunctionat

x=2

is

.A-1B0C1D2第11题单选题(1分)Thereisfunctionvaluetablex0124f(x)19233PleaseestablishNewtoninterpolationpolynomialnomorethanthreetimes.1）Constructadifferencequotienttable：xf(x)first-orderdifferencequotientsecond-orderdifferencequotientthird-orderdifferencequotient0119822314343-10aba,binthetablearerespectively

_________.

A-24,-27B-12,-15/2C8,-5/4D-8,-11/4第12题单选题(1分)Thereisfunctionvaluetable:x0123f(x)19113PleaseestablishNewtoninterpolationpolynomialnomorethanthreetimes.1）Constructadifferencequotienttable：xf(x)first-orderdifferencequotientsecond-orderdifferencequotientthird-orderdifferencequotient011982112-333-8-5-2/3ThenNewtoninterpolationpolynomial

is________.AN(x)=1+8x−3x(x−1)−23x(x−1)(x−2)BN(x)=−1−8x+3x(x−1)+23x(x−1)(x−2)CN(x)=3−8x−5x(x−1)−23x(x−1)(x−2)DN(x)=1+8x−3x2−23x3Chapter3_Unittest第1题单选题(1分)LetbeNewton-Cotesquadratureformula,then()A2B4C8D16第2题单选题(1分)CompositeCotesquadratureformulahastheconvergenceof（

）-order.A2B4C5D6第3题单选题(1分)Whenthestep

sizeisreducedtohalfoftheoriginalstepsizebyusingthe

compositeSimpsonquadratureformula,theremainderofthenew

approximationisapproximately(

)oftheremainderof

theoriginalapproximation.A1/4B1/16C1/32D1/64第4题单选题(1分),using

thelomborgalgorithm,weget_________。A3.015B3.03C3.04D3.06第5题单选题(1分)ThealgebraicprecisionofGaussquadratureformulawith3differentnodesis(

).A3B4C5D7第6题单选题(1分)Inorderto

makethequadratureformulahavethehighestalgebraicprecisionpossible,thevaluesofarerespectively()。ABCD第7题判断题(1分)Thealgebraicprecisionofinterpolationquadratureformula

withn

nodesisatleastn.第8题判断题(1分)ThequadraturecoefficientofCotesisindependentoftheintegrand,butrelatedtotheintervalofintegration.第9题判断题(1分)Thecompositequadratureformulaisusedtoavoidtherungephenomenonwhenthehigherorderpolynomialisusedtoapproximatetheoriginalfunction.

第10题判断题(1分)Rombergalgorithmisusedtospeeduptheconvergenceofnumericalintegrals。第11题判断题(1分)Gaussquadratureformulacanbeusedtoimprovethealgebraicaccuracy.第12题判断题(1分)Thequadratureformula

isGauss

formula.Chapter4_Unittest第1题单选题(1分)Thedichotomycalculationissimpleandconvenient,butitconvergesslowlyandcannotbesolved_____.AComplexrootsandevenmultiplerootsBComplexrootsandoddmultiplerootsCOddShigeDOddsumandevenShige第2题判断题(1分)Thestepwisesearchmethodissuitableforsolvingnonlinearequationsrequiringhighaccuracy.第3题判断题(1分)ThechoiceofinitialvalueaffectstheconvergenceofNewton'siterativemethod.第4题判断题(1分)Iff(x)iscontinuousat[a,b]

andf(a)f(b)<0,thenequationf(x)=0

hasonlyonerealzeroon(a,b).第5题单选题(1分)WhenusingtheAitkenmethod,howmanycorrectionsareneededfromxktoxk+1iteration?A1B2C3D4第6题单选题(1分)TheNewtoniterationmethodis_____convergentintherootdomain.AOneBTwoCThreeDFour第7题单选题(1分)Findingtheapproximatevalueof10canbetransformedintosolvingthequadraticequationx2−10=0byNewtoniterationmethod,then,takingx0=1.0,theniteratingoncetoget

x1=

__________.A2.0B3.5C4.0D5.5第8题单选题(1分)Solvetherootofequationf(x)=x3−3x2−x+9=0

in(-2,-1.5)

bysecantmethod,taketheinitialvaluex0=−2

,x1=−1

,anditerateoncetogetx2=_______.A-1B-1.4C-2.8D-3.5Chapter5_Unittest第1题单选题(1分)Solvethesystemofequationsusingthecolumnprincipaleliminationmethod.Forthefirstelimination,selecttheprincipal___________.

A3B4C-4D-9第2题单选题(1分)WhensolvingthelinearequationsbyLUdecompositionmethod,thesolutionisL=_________.

ABCD第3题单选题(1分)ThelinearequationgroupAX=0satisfiestheconclusion(

).

APossiblesolutionsBOnly0solutionsCNon-zerosolutionsDCertainsolutions第4题判断题(1分)Thedirectsolutionmethodistouseaseriesofformulastoperformfinite-stepcalculationsanddirectlyobtaintheexactsolutionofthesystemofequations.Therewillstillbeerrorsintheactualcalculationresults,suchasroundingerrors.第5题判断题(1分)AllmatricescanbeLUdecomposed第6题判断题(1分)Thecoefficientmatrixisprocessedbythecompleteprincipalelementeliminationmethod,whichwillnotaffecttheunknownvectorx.第7题判断题(1分)Thecolumnmainelementeliminationmethoddoesnotchangetheelementpositionofthematrixx.第8题判断题(1分)UsetheGauss-Jordaneliminationmethodtofindtheinverseofanymatrix.第9题判断题(1分)ThesquarerootdecompositionofthepositivedefinitematrixAexistsandisunique.第10题判断题(1分)Thesquarerootmethodwithoutselectingthemainelementisanumericalstabilityalgorithm.

第11题判断题(1分)ThecalculationamountofthesquarerootmethodisthesameasthecalculationamountofthegeneraldirectLUdecompositionmethod.

第12题判断题(1分)Allthematriceswithsequentialmainsub-formsgreaterthan0canbesquarerootdecomposed.

第13题判断题(1分)Thetridiagonalmatrixcanbetriangulatedaslongasthediagonalisdominant.

Chapter6_Unittest第1题单选题(1分)thevectornormsandarerespectively()A15,10B12,10C10,15D10,12第2题多选题(1分)Let,thenthefollowingstatementiscorrect(

)AB15C3D正确答案：AB第3题单选题(1分)TheJacobianiterativematrixforsolvinglinearsystemis(

)

ABCD第4题单选题(1分)TheGauss-Seideliterativematrixforsolvinglinearsystemis(

)ABCD第5题单选题(1分)Let,thenthespectralradiusof,=()A1B2C3D4第6题多选题(1分)Withequations(1)(2)TheJacobiiterativemethodandGauss-Seideliterativemethodoftheaboveequationsconvergeto_______.

A(1)Jacobiiterativemethodconverges,(2)JacobiiterativemethoddoesnotconvergeB(1)Jacobiiterativemethoddoesnotconverge,(2)JacobiiterativemethodconvergesC(1)Gauss-Seideliterativemethodconverges,(2)Gauss-SeideliterativemethoddoesnotconvergeD(1)Gauss-Seideliterativemethoddoesnotconverge,(2)Gauss-Seideliterativemethodconverges正确答案：BC第7题多选题(2分)Thefollowingstatementiscorrect()AForarandomlyselectedinitialvector,thenecessaryandsufficientconditionfortheiterativemethodtoconvergeisthatthespectralradiusofisBForiterativemethod,ifthereisacertainoperatornorm,theiterativemethodconverges;CIfconverges,then;DAisastrictlydiagonallydominantmatrix,thentheJacobiiterationmethodforthesolutionAx=b,andtheGauss-Seideliterationmethodbothconverge正确答案：ABD第8题判断题(1分)TheGauss-SeideliterativemethodcanberegardedasamodificationoftheJacobiiterativemethod第9题判断题(1分)TheGauss-SeideliterativemethodmustconvergefasterthantheJacobiiterativemethod(thesameinitialvector,thesameaccuracy,andfeweriterations)第10题判断题(1分)Thechoiceofinitialvaluewillaffecttheconvergenceoftheiterativemethodoflinearequations.第11题判断题(1分)Acertainnormoftheiterationmatrixislessthan1isanecessaryconditionforiterativeconvergence.第12题判断题(1分)UsetheSORiterativemethodtosolvethesystemofequationsAx=b.Aslongastherelaxationfactoris

0<ω<2,

thecorrespondingSORiterativemethodwillconverge.Chapter7_Unittest第1题单选题(1分)Whichofthefollowingisnotaconditionforthewell-posednessoftheinitialvalueproblemforthefirst-orderordinarydifferential

equations?AThesolutionexistsBThesolutionisuniqueCThesolutioncontinuouslydependsontheinitialvalueDTherearemultiplesolutions第2题单选题(1分)Ifthelocaltruncationerror

ofanalgorithm,thealgorithmissaidtohave(

)orderaccuracy.ApBp+1Cp+2Dp+3第3题单选题(1分)TakethestepsizeandwritetheforwardEulermethodtosolvetheinitialvalueproblem,thecalculationformula

is______________.()ABCD第4题单选题(1分)TakethestepsizeandusethebackwardEulermethodtosolvetheinitialvalueproblem:,

__________.

A-2B-1C0D1第5题单选题(1分)Theinitialsolutiontotheinitialvalueproblem

approximatesthetrapezoidalformula:yk+1≈()ABCD第6题单选题(1分)Theclassicalcalculationformulaofthefourth-orderRunge-Kutta

methodisyn+1=()ABCD第7题单选题(1分)Thelocaltruncationerrorandglobaltruncationerrorofthe4thorderRunge-Kuttamethodare:()ABCD第8题判断题(1分)Whenk=0,AdamsinterpolationmethodisEulermethod.第9题判断题(1分)TheR-Kmethodsareallimplicitmethods.第10题判断题(1分)Anyhigher-orderdifferentialequationcanbetransformedintoafirst-orderdifferentialequationproblemsolving.第11题判断题(1分)Theprecisionorderofthefour-levelR-Kmethodcanonlyreachuptothefourthorder.第12题判断题(1分)Analyticalsolutionstodifferentialequationsareoftennoteasytofind.Chapter8_Unittest第1题单选题(1分)Theanalytichierarchyprocessisa__________analyticalmethod.

AQualitativeBQuantitativeCQuantitativeDCombiningqualitativeandquantitative第2题单选题(1分)Inordertocomparetheimportanceofdifferentfactors,Saatyetal.proposedthe_____scaleforqualitativetoquantitativeconversion.A1-3B1-5C1-9D1-17第3题单选题(1分)Themaindifficultyinapplyinganalytichierarchyprocesstosolvetheproblemofsolutionevaluationis____.

AConstructionofpairwisecomparisonmatrixBCalculationofmatrixeigenvaluesandeigenvectorsCConsistencytestDCalculationofcombinationweightvector第4题判断题(1分)Theanalytichierarchyprocessissuitableformulti-objective,multi-criteriaorunstructureddecision-makingproblems.第5题判断题(1分)UsingAHPtomakedecisionscanleadtobetternewsolutions.第6题判断题(1分)Decision-makingreferstochoosingthebestplanthatthedecisionmakerconsidersbasedoncertaincriteriawhenfacedwithmultipleplans.第7题判断题(1分)Theanalytichierarchyprocessconstructsthepairwisecomparisonmatrixtoallowinconsistencies.第8题判断题(1分)Whentheevaluatorconstructsthepairwisecomparisonmatrix,itmainlydependsonhisownsubjectiveview.第9题判断题(1分)Theanalytichierarchyprocessisnotsuitableforproblemswithhighaccuracy.Chapter9_Unittest第1题判断题(1分)Eachevaluatedobjectinthecomprehensiveevaluationofteninvolvesonlyasingleindicator.第2题判断题(1分)Thefiveelementsthatconstitutethecomprehensiveevaluationproblemare:theevaluatedobject,theevaluationindex,theweightcoefficient,thecomprehensiveevaluationmodelandtheevaluator.第3题判断题(1分)Thelinearweightingsynthesismethodrequireseachevaluationindextobeindependentofeachother.

第4题判断题(1分)Thestandardizedtreatmentofevaluationindicatorsincludesthetreatmentofconsistencyanddimensionlesstreatment.Chapter10_Unittest第1题判断题(1分)Statisticalpredictionneedsthehelpofcomputers.第2题判断题(1分)