数值分析方法知到智慧树章节测试课后答案2024年秋浙江大学

数值分析方法知到智慧树章节测试课后答案2024年秋浙江大学第一章单元测试

Whentheerrorpropagationformulais,itiscalledexponentialerrorpropagation.()

A:错B:对

答案:错Whenperforming（）operationwithtwosimilarnumbers,itiseasytocauselargererrors.（

A:Subtraction

B:Division

C:Multiplication

D:Addition

答案:Subtraction

Whichproblemsshouldbesolvedbynumericalanalyticaltool()?

A:

B:

C:

D:

答案:

；

Ifp*=10.001isanapproximateofp=10.000,thentherelativeerroris()

A:

B:

C:

D:

答案:

Toapproach1/3,weshoulduseatleast()significantdigitstoguaranteearelativeerrorof

A:

B:

C:

D:

答案:

第二章单元测试

Supposeisasequencethatconvergestop,withforalln.Ifpositiveconstantsandexistwith

.

Then,if,thesequenceislinearlyconvergent.()

A:错B:对

答案:对Theconvergencerateofthebisectionmethodis（）.

A:

B:

C:

D:

答案:

TheconvergencerateoftheNewton’smethodis（）.

A:

B:

C:

D:

答案:

Letand.UseNewton’smethodtofind.canbeusedasaninitialpoint?（）

A:错B:对

答案:错Thefixed-pointproblemg(x)=x-x3-4x2+10cannotconvergeforinitialpointx0=1.5.（）

A:错B:对

答案:对

第三章单元测试

IfavectorsequenceconvergestoXintheL1norm,italsoconvergestoXinthenorm.（）

A:对B:错

答案:对Asufficientconditionfortheexistenceofauniquefixedpointiswithinagiveninterval.（）

A:错B:对

答案:错Whentheinitialvalueisincorrectlyselected,bothfixed-pointiterationandNewton’smethodwillfailtoconverge.（）

A:错B:对

答案:对Beginningwith,theseconditerationofNewton’smethodfortheequationis0.6860.()

A:对B:错

答案:对Theconvergencerateofthefixed-pointiterativemethodis（）.

A:

B:

C:

D:

答案:

第四章单元测试

IfAissymmetric,then.（）

A:错B:对

答案:对Giventhelinearsystem

TheGauss-Seidelalgorithmcanbeusedtosolvethesystem.()

A:对B:错

答案:对IfthespectralradiusofamatrixAsatisfies,thenAisaconvergentmatrix.()

A:错B:对

答案:对Theiterativecalculationformulaforlinearproblemsis,theiterativeprocesscanconvergewhenTsatisfieswhichofthefollowingconditions?（）

A:ThespectralradiusofTislessthan1.

B:nislargeenough,theL2normofissmallenough

C:Tisaconvergentmatrix

D:nislargeenough,theL1normofissmallenough

答案:ThespectralradiusofTislessthan1.

；nislargeenough,theL2normofissmallenough

；Tisaconvergentmatrix

；nislargeenough,theL1normofissmallenough

Fortheiterativesolutionoflinearproblems,theJacobialgorithmalwaysconvergefasterthantheGauss-Seidelalgorithm.（）

A:错B:对

答案:错

第五章单元测试

Passingnpoints,apolynomialwithdegreenomorethannthatsatisfiestheinterpolationconditionsexistsandisunique.（）

A:错B:对

答案:错Whichofthefollowingstatementsarecorrectaboutpolynomialfitting?（）

A:Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

B:Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

C:Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

D:Inaclosedinterval,thereisnopolynomialfunctiontoapproximatetheexponentialfunctionwithsufficientprecision

答案:Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

；Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

；Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

Letbetheinterpolationpolynomialforthedata(0,0),(0.5,y),(1,3),and(2,2).Thecoefficientofinis6.Theny=4.25.()

A:对B:错

答案:对ConstructtheLagrangeinterpolatingpolynomialofdegree2forthegivenvaluesofxandy:

Theny=6.712whenx=4.8.()

A:对B:错

答案:对WritethelinearLagrangeinterpolatingpolynomialthatpassesthroughthepoints(2;4)and(5;1).Thenf(7)={2}.()

A:错B:对

答案:错Thegoalofleastsquaresapproximationminimizesthe（）normoftheerror.()

A:

B:

C:

D:

答案:

第六章单元测试

Theerrorofthethree-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,boththefive-pointandthree-pointnumericaldifferentiationmethodshavethesameoptimalsteplengthh.()

A:错B:对

答案:错Theerrorofthefive-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,thelargertheh,thehighertheprecisionofthenumericaldifferentiation.（）

A:错B:对

答案:错UsingRichardson'sextrapolationmethod,low-orderformulascanbeusedtoderivehigh-orderformulasforsolvingnumericaldifferentials.（）

A:对B:错

答案:对

第七章单元测试

Theerrororderofthetrapezoidalintegralformulais（）。

A:

B:

C:

D:

答案:

Theerrororderofthecompositetrapezoidalintegralformulais（）.

A:

B:

C:

D:

答案:

TheSimpson’srulehasadegreeofprecision2.()

A:错B:对

答案:错RombergintegralistheapplicationofRichardsonextrapolationinnumericalintegration.()

A:对B:错

答案:对Thequadratureformulaisexactforallpolynomialsofdegreelessthanorequalto2.Then,c0=1/3,c1=4/3,c2=1/3.()

A:对B:错

答案:对

第八章单元测试

WhichofthefollowingfunctionsarenotLipschitzcontinuouson[0,1]?（）。

A:

B:

C:

D:

答案:

；

ThelocaltruncationerrorofEuler'smethodis（）.

A:

B:

C:

D:

答案: