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1、MATLAB牛頓法源代碼function[sol,it_hist,ierr]=nsol(x,f,tol,parms)%Newtonsolver,locallyconvergent%solverforf(x)=0%%HybridofNewton,Shamanskii,Chord%%C.T.Kelley,November26,1993%%Thiscodecomeswithnoguaranteeorwarrantyofanykind.%%function[sol,it_hist,ierr]=nsol(x,f,tol,parms)%%inputs:%???????initialiterate=
2、x%??function=f%???????tol=[atol,rtol]relative/absolute%???errortolerances%parms=[maxit,isham,rsham]%???maxit=maxmiumnumberofiterations%????default=40%??isham,rsham:TheJacobianmatrixis%??computedandfactoredafterisham%??????????????updatesofxorwhenevertheratio%??ofsuccessiveinfinitynormsofthe%????
3、??????????nonlinearresidualexceedsrsham.%???isham=1,rsham=0isNewton'smethod,%???isham=-1,rsham=1isthechordmethod,%???isham=m,rsham=1istheShamanskiimethod%????????????defaults=[40,1000,.5]%%output:%sol=solution%it_hist=infinitynormsofnonlinearresiduals%???fortheiteration%ierr=0uponsuccessfultermi
4、nation%ierr=1ifeitheraftermaxititerations%????????????theterminationcriterionisnotsatsified%????????????ortheratioofsuccessivenonlinearresiduals%????????????exceeds1.Inthislattercase,theiteration%????isterminted.%%%internalparameter:%??????debug=turnson/offiterationstatisticsdisplayas%??????????
5、????theiterationprogresses%%Requires:diffjac.m,dirder.m%%Hereisanexample.Theexamplecomputespiasarootofsin(x)%withNewton'smethodandplotstheiterationhistory.%%%x=3;tol=[1.d-6,1.d-6];params=[40,1,0];%[result,errs,it_hist]=nsol(x,'sin',tol,params);%result%semilogy(errs)%%%setthedebugparameter,1turns
6、displayon,otherwiseoff%debug=0;%%initializeit_hist,ierr,andsettheiterationparameters%ierr=0;maxit=40;isham=1000;rsham=.5;ifnargin==4maxit=parms(1);isham=parms(2);rsham=parms(3);endrtol=tol(2);atol=tol(1);it_hist=[];n=length(x);fnrm=1;itc=0;%%evaluatefattheinitialiterate%computethestoptolerance%f
7、0=feval(f,x);fnrm=norm(f0,inf);it_hist=[it_hist,fnrm];fnrmo=1;itsham=isham;stop_tol=atol+rtol*fnrm;%%mainiterationloop%while(fnrm>stop_tol&itc
