clear
close all
figure(1)
x=0:0.01:1;
plot(x,x-cos(x)),grid
a=0; b=1;
fa=a-cos(a);
fb=b-cos(b);
n=10;
for jj=1:n
    m=(a+b)/2;
    mm(jj)=(a+b)/2;
    akurve(jj)=a;
    bkurve(jj)=b;
    fm=m-cos(m);
    fmid(jj)=fm;
    if sign(fa)==sign(fm), a=m;
    else b=m; end
end
xbisection=mm;
x=1:n;
figure(2)
plot(x,mm,'.k',x,akurve,'*r',x,bkurve,'*r')

xold=0.5;
xnewton(1)=xold;
fnewton(1)=xold-cos(xold);
for jj=1:n
    xny=xold-(xold-cos(xold))/(1+sin(xold));
    xold=xny;
    xnewton(jj+1)=xold;
    fnewton(jj+1)=xold-cos(xold);
end
format long
xbisection
xnewton
format
x=0.73908513321515;
figure(3)
subplot(2,1,1)
xakse=1:n;
plot(xakse,abs(x-xbisection),'.',xakse,abs(x-xnewton(1:end-1)),'.')
subplot(2,1,2)
plot(xakse,abs(x-xbisection)/x,'.',xakse,abs(x-xnewton(1:end-1))/x,'.')