MIT流体力学课件2

《MIT流体力学课件2》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、IntroductiontoNumericalAnalysisforEngineers•FundamentalsofDigitalComputing–DigitalComputerModels–Convergence,accuracyandstability–Numberrepresentation–Arithmeticoperations–Recursionalgorithms•ErrorAnalysis–Errorpropagation–numericalstability–Errorestimation–Errorcancell

2、ation–Conditionnumbers2.29NumericalMarineHydrodynamicsLecture2FloatingNumberRepresentationmMantissabBaseeExponentExamplesDecimalBinaryConventionDecimalMaxmantissaMinmantissaBinaryMaxexponentGeneralMinexponent2.29NumericalMarineHydrodynamicsLecture2ErrorAnalysisNumberRep

3、resentationAdditionandSubtractionAbsoluteErrorShiftmantissaoflargestnumberRelativeErrorResulthasexponentoflargestnumberAbsoluteErrorRelativeErrorUnboundedMultiplicationandDivisionRelativeErrorBounded2.29NumericalMarineHydrodynamicsLecture2DigitalArithmeticsFiniteMantiss

4、aLengthfunctionc=radd(a,b,n)%radd.m%functionc=radd(a,b,n)%%Addstworealnumbersaandbsimulatinganarithmeticunitwith%nsignificantdigits.%%Firstdeterminesignsa=sign(a);Limitedprecisionsb=sign(b);if(sa==0)additioninMATLABla=-200;elsela=ceil(log10(sa*a*(1+10^(-(n+1)))));endif(

5、sb==0)lb=-200;elselb=ceil(log10(sb*b*(1+10^(-(n+1)))));endlm=max(la,lb);f=10^(n);at=sa*round(f*sa*a/10^lm);bt=sb*round(f*sb*b/10^lm);ct=at+bt;sc=sign(ct);if(sc~=0)if(log10(sc*ct)>=n)ct=round(ct/10)*10;endendc=ct*10^lm/f;2.29NumericalMarineHydrodynamicsLecture2RecursionH

6、eron’sDevicea=26;n=10;MATLABscriptg=1;Numericallyevaluatesquare-root%NumberofDigitsheron.mdig=5;sq(1)=g;fori=2:nsq(i)=0.5*radd(sq(i-1),a/sq(i-1),dig);Initialguessendholdoffplot([0n],[sqrt(a)sqrt(a)],'b')holdonTestplot(sq,'r')plot(a./sq,'r-.')plot((sq-sqrt(a))/sqrt(a),'g

7、')gridonMeanofguessanditsreciprocalRecursionAlgorithm2.29NumericalMarineHydrodynamicsLecture2RecursionHorner’sSchemeEvaluatepolynomialhorner.m%Hornersscheme%forevaluatingpolynomialsa=[12345678910];n=length(a)-1;Horner’sSchemez=1;b=a(1);%Noteindexshiftforafori=1:nb=a(i+1

8、)+z*b;endp=bGeneralordern>>hornerp=Recurrencerelation55>>2.29NumericalMarineHydrodynamicsLecture2RecursionOrde