Matlab - Numerical Analysis with MATLAB

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MATLABhasmanytoolsthatmakethispackagewellsuitedfornumericalcomputations.Thistutorialdealswiththerootfinding,interpolation,numericaldifferentiationandintegrationandnumericalsolutionsoftheordinarydifferentialequations.Numericalmethodsoflineara

2、lgebraarediscussedinTutorial4.
 
FunctionDescriptionabsAbsolutevaluedblquadNumericallyevaluatedoubleintegralerfErrorfunctionfevalExecutefunctionspecifiedbystringfzeroScalarnonlinearzerofindinggammaGammafunctioninlineConstructINLINEobjectinterp1One-dimensionali

3、nterpolationinterp2Two-dimensionalinterpolationlinspaceEvenlyspacedvectormeshgridXandYarraysfor3-DplotsnormMatrixorvectornormode23Solvenon-stiffdifferentialequationsode45Solvenon-stiffdifferentialequationsode113Solvenon-stiffdifferentialequationsode15sSolvestiffdifferentialequationsode2

4、3sSolvestiffdifferentialequationspolyConvertrootstopolynomialpolyvalEvaluatepolynomialppvalEvaluatepiecewisepolynomialquadNumericallyevaluateintegral,lowordermethodquad8Numericallyevaluateintegral,higherordermethodrcondReciprocalconditionestimatorrootsFindpolynomialrootssplineCubicsplin

5、edatainterpolationsurf3-DcoloredsurfaceunmkppSupplydetailsaboutpiecewisepolynomial2!"#Acentralproblemdiscussedinthissectionisformulatedasfollows.Givenareal-valuedfunctionnnf:


,n
1,findavectorrsothatf(r)=0.Vectorriscalledtherootorzerooff.5.2.1Computingrootsoftheunivariatepolyn

6、omialsPolynomialsarerepresentedinMATLABbytheircoefficientsinthedescendingorderofpowers.32Forinstance,thecubicpolynomialp(x)=3x+2x-1isrepresentedasp=[3201];Itsrootscanbefoundusingfunctionrootsformatlongr=roots(p)r=-1.000000000000000.16666666666667+0.55277079839257i0.16666666666667-0.5527

7、7079839257iTocheckcorrectnessofthisresultweevaluatep(x)atrusingfunctionpolyvalerr=polyval(p,r)err=1.0e-014*0.222044604925030+0.01110223024625i0-0.01110223024625iToreconstructapolynomialfromitsrootsonecanusefunctionpoly.Usingtherootsrcomputedearlierweobtainpoly(r)ans=1.000000000