task4summerpractice

%met_hord
function [z, k] = metod_hord(g, dg, x, eps)
for i=1:length(x)
    z(i)=x(i);
    k(i)=1;
    while(abs(g(z(i),i))>eps)
        k(i)=k(i)+1;
        if(k(i)==2)
            z(i)=z(i)-g(z(i),i)/dg(z(i));
        else
            z(i)=(x(i)*g(z(i),i)-z(i)*g(x(i),i))/(g(z(i),i)-g(x(i),i));
        end
    end
end
end

%met_sek
function [z, k] = metod_sek(g, dg, x, eps)
for i=1:length(x)
    z(i)=x(i);
    z_0 = x(i);
    k(i)=1;
    while(abs(g(z(i),i))>eps)
        k(i)=k(i)+1;
        if(k(i)==2)
            z_1=x(i)-g(x(i),i)/dg(x(i));
        else
            z(i)=z_1-(z_1-z_0)*g(z_1,i)/(g(z_1,i)-g(z_0,i));
        end
        z_0=z_1;
        z_1=z(i);
    end
end
end

%main
a=0; b=1.2; h=0.12; eps = 10^(-8);
x=a:h:b;
n=length(x)-1;
S = taylor_series_task1(x,eps);
for i=0:n
    %F(i+1)=S(1)+i*(S(11)-S(1))/n;
    F(i+1)=S(1)+i*(S(length(x))-S(1))/n;
end
g = @(z, i) taylor_series_task1(z, eps)-F(i);
dg = @(z) sin(pi*z^2/2);
%z = metod_kas(g,dg,x,eps);
z = metod_sek(g,dg, x,eps);
%z = metod_hord(g,dg, x,eps);
plot(x,S);
hold on
plot(F,z)