數(shù)值分析方法智慧樹知到課后章節(jié)答案2023年下浙江大學(xué)

數(shù)值分析方法智慧樹知到課后章節(jié)答案2023年下浙江大學(xué)浙江大學(xué)

第一章測(cè)試

Whentheerrorpropagationformulais,itiscalledexponentialerrorpropagation.()

A:對(duì)B:錯(cuò)

答案:錯(cuò)

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:

第二章測(cè)試

Supposeisasequencethatconvergestop,withforalln.Ifpositiveconstantsandexistwith

.

Then,if,thesequenceislinearlyconvergent.()

A:對(duì)B:錯(cuò)

答案:對(duì)

Theconvergencerateofthebisectionmethodis（）.

A:

B:

C:

D:

答案:

TheconvergencerateoftheNewton’smethodis（）.

A:

B:

C:

D:

答案:

Letand.UseNewton’smethodtofind.canbeusedasaninitialpoint?（）

A:錯(cuò)B:對(duì)

答案:錯(cuò)

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

A:錯(cuò)B:對(duì)

答案:對(duì)

第三章測(cè)試

IfavectorsequenceconvergestoXintheL1norm,italsoconvergestoXinthenorm.（）

A:對(duì)B:錯(cuò)

答案:對(duì)

Asufficientconditionfortheexistenceofauniquefixedpointiswithinagiveninterval.（）

A:對(duì)B:錯(cuò)

答案:錯(cuò)

Whentheinitialvalueisincorrectlyselected,bothfixed-pointiterationandNewton’smethodwillfailtoconverge.（）

A:錯(cuò)B:對(duì)

答案:對(duì)

Beginningwith,theseconditerationofNewton’smethodfortheequationis0.6860.()

A:對(duì)B:錯(cuò)

答案:對(duì)

Theconvergencerateofthefixed-pointiterativemethodis（）.

A:

B:

C:

D:

答案:

第四章測(cè)試

IfAissymmetric,then.（）

A:對(duì)B:錯(cuò)

答案:對(duì)

Giventhelinearsystem

TheGauss-Seidelalgorithmcanbeusedtosolvethesystem.()

A:對(duì)B:錯(cuò)

答案:對(duì)

IfthespectralradiusofamatrixAsatisfies,thenAisaconvergentmatrix.()

A:錯(cuò)B:對(duì)

答案:對(duì)

Theiterativecalculationformulaforlinearproblemsis,theiterativeprocesscanconvergewhenTsatisfieswhichofthefollowingconditions?（）

A:ThespectralradiusofTislessthan1.

B:Tisaconvergentmatrix

C:nislargeenough,theL1normofissmallenough

D:nislargeenough,theL2normofissmallenough

答案:ThespectralradiusofTislessthan1.

;Tisaconvergentmatrix

;nislargeenough,theL1normofissmallenough

;nislargeenough,theL2normofissmallenough

Fortheiterativesolutionoflinearproblems,theJacobialgorithmalwaysconvergefasterthantheGauss-Seidelalgorithm.（）

A:對(duì)B:錯(cuò)

答案:錯(cuò)

第五章測(cè)試

Passingnpoints,apolynomialwithdegreenomorethannthatsatisfiestheinterpolationconditionsexistsandisunique.（）

A:錯(cuò)B:對(duì)

答案:錯(cuò)

Whichofthefollowingstatementsarecorrectaboutpolynomialfitting?（）

A:Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

B:Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

C:Inaclosedinterval,thereisnopolynomialfunctiontoapproximatetheexponentialfunctionwithsufficientprecision

D:Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

答案:Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

;Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

;Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

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

A:錯(cuò)B:對(duì)

答案:對(duì)

ConstructtheLagrangeinterpolatingpolynomialofdegree2forthegivenvaluesofxandy:

Theny=6.712whenx=4.8.()

A:錯(cuò)B:對(duì)

答案:對(duì)

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

A:對(duì)B:錯(cuò)

答案:錯(cuò)

Thegoalofleastsquaresapproximationminimizesthe（）normoftheerror.()

A:

B:

C:

D:

答案:

第六章測(cè)試

Theerrorofthethree-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,boththefive-pointandthree-pointnumericaldifferentiationmethodshavethesameoptimalsteplengthh.()

A:錯(cuò)B:對(duì)

答案:錯(cuò)

Theerrorofthefive-pointnumericaldifferentiationmethodis（）。

A:

B:

C:

D:

答案:

Whenconsideringtheroundingerror,thelargertheh,thehighertheprecisionofthenumericaldifferentiation.（）

A:對(duì)B:錯(cuò)

答案:錯(cuò)

UsingRichardson'sextrapolationmethod,low-orderformulascanbeusedtoderivehigh-orderformulasforsolvingnumericaldifferentials.（）

A:對(duì)B:錯(cuò)

答案:對(duì)

第七章測(cè)試

Theerrororderofthetrapezoidalintegralformulais（）。

A:

B:

C:

D:

答案:

Theerrororderofthecompositetrapezoidalintegralformulais（）.

A:

B:

C:

D:

答案:

TheSimpson’srulehasadegreeofprecision2.()

A:對(duì)B:錯(cuò)

答案:錯(cuò)

RombergintegralistheapplicationofRichardsonextrapolationinnumericalintegration.()

A:對(duì)B:錯(cuò)

答案:對(duì)

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

A:錯(cuò)B:對(duì)

答案:對(duì)

第八章測(cè)試

WhichofthefollowingfunctionsarenotLipschitzcontinuouson[0,1]?（）。

A:

B:

C:

D:

答案:

;

ThelocaltruncationerrorofEuler'smethodis（）.

A:

B:

C:

D:

答案:

T