LMA

非线性最小二乘法Levenberg-Marquardt-method

Levenberg-MarquardtMethod(麦夸尔特法)

Levenberg-MarquardtisapopularalternativetotheGauss-Newtonmethodoffindingtheminimumofa

functionthatisasumofsquaresofnonlinea折纸作品 rfunctions,

LettheJacobianofbedenoted,thentheLevenberg-Marquardtmethodarchesinthe

directiongivenbythesolutiontotheequations

hodhasthenicepropertythat,for

somescalarrelatedto,thevector政府首脑 isthesolutionoftheconstrainedsubproblemofminimizing

subjectto(Gilletal.1981,p.136).

ThemethodisudbythecommandFindMinimum[f,x,x0]whengiventheMethod->LevenbergMarquardtoption.

SEEALSO:Minimum,OptimizationREFERENCES:

Bates,ts,k:Wiley,1988.

Gill,P.R.;Murray,W.;andWright,M.H."TheLevenberg-

MarquardtMethod.":AcademicPress,pp.136-137,1981.

Levenberg,K."AMethodfortheSolutionofCertain

ProblemsinLeastSquares.".2,164-168,1944.

Marquardt,D."AnAlgorithmforLeast-SquaresEstimationofNonlinearParameters.".11,431-441,1963.

Levenberg–Marquardtalgorithm

FromWikipedia,thefreeencyclopediaJumpto:navigation,arch

Inmathematicsandcomputing,theLevenberg–Marquardt

algorithm(LMA)[1]providesanumericalsolutiontotheproblem

ofminimizingafunction,generallynonlinear,overaspaceof

inimizationproblemsari

especiallyinleastsquarescurvefittingandnonlinearprogramming.

TheLMAinterpolatesbetweentheGauss–Newtonalgorithm

(GNA)ismore

robustthantheGNA,whichmeansthatinmanycasitfindsa

l-

behavedfunctionsandreasonablestartingparameters,theL梦见被人杀 MA

alsobeviewed

asGauss–Newtonusingatrustregionapproach.

TheLMAisave恼怒的反义词 rypopularcurve-fittingalgorithmudin

r,theLMAfindsonlyalocalminimum,nota

globalminimum.

Contents[hide]

1CaveatEmptor

2Th如今的近义词 eproblem3Thesolution

o3.1Choiceofdampingparameter

4Example

5Notes

6Seealso

7References

8Externallinks

o8.1Descriptions

o8.2Implementations[edit]CaveatEmptor

Oneimportantlimitationthatisve工作评语 ryoftenover-lookedis

thatitonlyoptimisforresidualerrorsinthedependantvariable

(y).Ittherebyimplicitlyassumesthatanyerrorsinthe

independentvariablearezerooratleastratioofthetwoisso

notadefect,itisintentional,but

itmustbetakenintoaccountwhendecidingwhethertouthis

hismaybesuitableincontexto千足金和万足金的区别 fa

controlledexperimenttherearemanysituationswherethis

situationithernon-least

squaresmethodsshouldbeudortheleast-squaresfitshould

bedoneinproportiontotherelativeerrorsinthetwovariables,

notsimplythevertical"y"gtorecognithiscanlead

toafitwhichissignificantlyincorrectandfundamentallywrong.

yormaynotbeobvioustotheeye.

MicroSoftExcel'schartoffersatrendfitthathasthis

ftenfallintothistrap

assumingthefitiscorrectlycalculatedforallsituations.

O钢琴级别怎么划分 penOfficespreadsheetcopiedthisfeatureandprentsthesameproblem.

[edit]Theproblem

TheprimaryapplicationoftheLevenberg–Marquardt

algorithmisintheleastsquarescurvefittingproblem:givenat

ofmempiricaldatumpairsofindependentanddependent

variables,(xi,yi),optimizetheparametersofthemodelcurve

f(x,)sothatthesumofthesquaresofthedeviations

becomesminimal.[edit]Thesolution

Likeothernumericminimizationalgorithms,theLevenberg–

ta

minimization,theurhastoprovideaninitialguessforthe

parametervector,.Inmanycas,anuninformedstandard

guesslikeT=(1,1,...,1)willworkfine;

inothercas,thealgorithmconvergesonlyiftheinitialguessisalreadysomewhatclotothefinalsolution.