Matlab 求根代码 包括Newton法、Secant法、Steffenson法、Aitken's法、不动点迭代法。

% main.m result = zeros(6,6); iteration = zeros(6,6); format compact % This shortens the output. format long % This prints more decimal places. i = 1; enable = zeros(6,1); enable(1,1)=1; enable(2,1)=1; enable(3,1)=1; enable(4,1)=1; enable(5,1)=1; enable(6,1)=1; leftbound = 0; rightbound = 8; step = 0.1; fcleftbound = 18; fcrightbound =fcleftbound; for fc=fcleftbound:fcrightbound x=leftbound:step:rightbound for x0=leftbound:step:rightbound fcp = 1000+fc; esp = 1e-5; %x0 = 3; localvalue1 = []; localvalue2 = []; localvalue3 = []; localvalue4 = []; localvalue5 = []; localvalue6 = []; if enable(1,1)==1 [result(1,i), iteration(1,i),localvalue1] = Steffensen(fc,x0,esp); end if enable(2,1)==1 [result(2,i), iteration(2,i),localvalue2] = newton(x0,fc,fcp,esp); end if enable(3,1)==1 [result(3,i), iteration(3,i),localvalue3] = secant(x0,x0-0.0001,fc,esp); end if enable(4,1)==1 [result(4,i), iteration(4,i),localvalue4] = FixedPointIter(fc,x0,esp); end if enable(5,1)==1 [result(5,i), iteration(5,i),localvalue5] = Steffensen_diff(fc,fcp,x0,esp); end if enable(6,1)==1 [result(6,i), iteration(6,i),localvalue6] = Aitken(fc,x0,esp); end i=i+1; %fc %x0 %esp %result %iteration %disp(['----------------------------------']) end %x=0:1:20; switch(fc) case 9 functionstr = ['sqrt(10/(x+4))-x']; case 12 functionstr=['(2-exp(x)+x^2)/3-x ']; case 13 functionstr=['0.5*(sin(x)+cos(x))-x']; case 14 functionstr=['sqrt(exp(x)/3)-x']; case 15 functionstr=['5\^(-x)-x']; case 16 %ex 7 functionstr=['x\^3-x-1']; case 17 %ex 8 functionstr = ['x-2\^(-x)']; case 5 functionstr = ['0.01*(p^3-3*p^2+3*p-1)']; otherwise functionstr=['']; end figure; title(['f(x)= ' functionstr ' - initial guess - iteration times graph']);hold on; xlabel(['initial guess number']);ylabel(['iteration times']); if enable(1,1)==1 h=plot(x,iteration(1,:),'r-');set(h,'LineWidth',3);hold on; end if enable(2,1)==1 h=plot(x,iteration(2,:),'b-');set(h,'LineWidth',2);hold on; end if enable(3,1)==1 h=plot(x,iteration(3,:),'g-');set(h,'LineWidth',2);hold on; end if enable(4,1)==1 h=plot(x,iteration(4,:),'c-');set(h,'LineWidth',2);hold on; end if enable(6,1)==1 h=plot(x,iteration(6,:),'m-');set(h,'LineWidth',2);hold on; end if enable(5,1)==1 h=plot(x,iteration(5,:),'ko-');set(h,'LineWidth',1);hold on; end legend('Steffensen-g(x)=x+f(x)','newton','secant','FixedPointIterator','Aitken method','Steffensen-Newton',-1); figure; title(['f(x)= ' functionstr ' initial guess - result graph']);hold on; xlabel(['initial guess number']);ylabel(['result']); if enable(1,1)==1 h=plot(x,result(1,:),'r-');set(h,'LineWidth',3);hold on; end if enable(2,1)==1 h=plot(x,result(2,:),'b-');set(h,'LineWidth',2);hold on; end if enable(3,1)==1 h=plot(x,result(3,:),'g-');set(h,'LineWidth',2);hold on; end if enable(4,1)==1 h=plot(x,result(4,:),'c-');set(h,'LineWidth',2);hold on; end if enable(6,1)==1 h=plot(x,result(6,:),'m-');set(h,'LineWidth',2);hold on; end if enable(5,1)==1 h=plot(x,result(5,:),'ko-');set(h,'LineWidth',1);hold on; end legend('Steffensen-g(x)=x+f(x)','newton','secant','FixedPointIterator','Aitken method','Steffensen-Newton',-1); %legend('Steffensen-g(x)=x+f(x)','newton','secant','FixedPointIterator','Aitken method',-1); end