數(shù)值分析方法知到章節(jié)答案智慧樹(shù)2023年浙江大學(xué)

數(shù)值分析方法知到章節(jié)測(cè)試答案智慧樹(shù)2023年最新浙江大學(xué)第一章測(cè)試

Whentheerrorpropagationformulais,itiscalledexponentialerrorpropagation.()

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Whenperforming（）operationwithtwosimilarnumbers,itiseasytocauselargererrors.（

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Subtraction

Whichproblemsshouldbesolvedbynumericalanalyticaltool()?

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;

Ifp*=10.001isanapproximateofp=10.000,thentherelativeerroris()

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Toapproach1/3,weshoulduseatleast()significantdigitstoguaranteearelativeerrorof

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第二章測(cè)試

Supposeisasequencethatconvergestop,withforalln.Ifpositiveconstantsandexistwith

.

Then,if,thesequenceislinearlyconvergent.()

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Theconvergencerateofthebisectionmethodis（）.

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TheconvergencerateoftheNewton’smethodis（）.

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Letand.UseNewton’smethodtofind.canbeusedasaninitialpoint?（）

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

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第三章測(cè)試

Asufficientconditionfortheexistenceofauniquefixedpointiswithinagiveninterval.（）

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Whentheinitialvalueisincorrectlyselected,bothfixed-pointiterationandNewton’smethodwillfailtoconverge.（）

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Beginningwith,theseconditerationofNewton’smethodfortheequationis0.6860.()

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Theconvergencerateofthefixed-pointiterativemethodis（）.

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IfavectorsequenceconvergestoXintheL1norm,italsoconvergestoXinthenorm.（）

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第四章測(cè)試

IfAissymmetric,then.（）

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Giventhelinearsystem

TheGauss-Seidelalgorithmcanbeusedtosolvethesystem.()

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IfthespectralradiusofamatrixAsatisfies,thenAisaconvergentmatrix.()

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Theiterativecalculationformulaforlinearproblemsis,theiterativeprocesscanconvergewhenTsatisfieswhichofthefollowingconditions?（）

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nislargeenough,theL2normofissmallenough

;ThespectralradiusofTislessthan1.

;nislargeenough,theL1normofissmallenough

;Tisaconvergentmatrix

Fortheiterativesolutionoflinearproblems,theJacobialgorithmalwaysconvergefasterthantheGauss-Seidelalgorithm.（）

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第五章測(cè)試

Passingnpoints,apolynomialwithdegreenomorethannthatsatisfiestheinterpolationconditionsexistsandisunique.（）

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Whichofthefollowingstatementsarecorrectaboutpolynomialfitting?（）

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Oneoftheadvantagesofpolynomialfittingisthatthealgebraicoperationsofpolynomialsarestillpolynomials

;Thepolynomialwiththehighestdegreen-1whichpassthroughngivenpointsisunique

;Taylorpolynomialscanonlyapproximateafunctionatacertainpoint

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

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ConstructtheLagrangeinterpolatingpolynomialofdegree2forthegivenvaluesofxandy:

Theny=6.712whenx=4.8.()

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

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Thegoalofleastsquaresapproximationminimizesthe（）normoftheerror.()

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第六章測(cè)試

Theerrorofthethree-pointnumericaldifferentiationmethodis（）。

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Whenconsideringtheroundingerror,boththefive-pointandthree-pointnumericaldifferentiationmethodshavethesameoptimalsteplengthh.()

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Theerrorofthefive-pointnumericaldifferentiationmethodis（）。

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Whenconsideringtheroundingerror,thelargertheh,thehighertheprecisionofthenumericaldifferentiation.（）

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

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第七章測(cè)試

Theerrororderofthetrapezoidalintegralformulais（）。

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Theerrororderofthecompositetrapezoidalintegralformulais（）.

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TheSimpson’srulehasadegreeofprecision2.()

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RombergintegralistheapplicationofRichardsonextrapolationinnumericalintegration.()

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

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第八章測(cè)試

WhichofthefollowingfunctionsarenotLipschitzcontinuouson[0,1]?（）。

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;

ThelocaltruncationerrorofEuler'smethodis（）.

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Thelocaltruncation