1. Njutn
f1 = @(x)x.^2-1;
f2 = @(x)sin(x);
fplot(f1, 'r');
hold on
grid on
fplot(f2,'b');
hold off
f = @(x)x.^2-1-sin(x);
a = 1;
b = 2;
if f(a)*f(b) <= 0
  disp('Dobar interval izolacije');
end
f(a)
f(b)
syms x;
fs = sym(f)
df1s = diff(fs, x);
df2s = diff(fs, x, 2);
f = matlabFunction(fs);
df1 = matlabFunction(df1s);
df2 = matlabFunction(df2s);
if f(a)*df2(a) > 0
    	x0 = a;
else
    	x0 = b;
end
disp(x0)
dnf(a) i dnf(b)
tol = 1e-4; 
x = x0
fx = f(x) 
i = 1;
while abs(f(x))/m1 >= tol
    	x = x - f(x)/df1(x);
    	fx = f(x);
    	fprintf('%.6f   %.6f\n',x,fx);
    	i = i + 1;
end

Polovljenje
tol = 1e-4;
n = ceil(log((b-a)/tol)/log(2)-1);
disp(n)
x = (a+b)/2
fx = f(x)
for i = 1:n
    if f(a)*fx>0
        a = x;
    else
        b = x;
    end
    x = (a+b)/2;
    fx = f(x);
    fprintf('%.6f   %.6f\n',x,fx);
end

2. Jakobi
A = [6 -2 -2; -1 7 -1; 1 1 5];
b = [16 20 -4]';
tol = 1e-3;
D = diag(diag(A));
B = D\(D-A);
c = D\b;
Bnorm = norm(B, inf);
cnorm = norm(c, 'inf');
n = ceil(log((1-Bnorm)*tol/cnorm)/log(Bnorm)-1);
x = c;
disp(x');
for i = 1:n
    xOld = x;
    x = B*x+c;
    disp(x');
    if norm(x-xOld, 'inf') < (1-Bnorm)*tol/Bnorm
        break
    end
end

Gaus
A = [4 1 -2; 1 -5 3; 2 1 4];
b = [9 4 -1]';
n = 12;
D = diag(diag(A));
B = D\(D-A);
c = D\b
B1 = tril(B)
B2 = triu(B)
I = eye(3);
x = c;
disp(x');
for i = 1:n
    x = (I-B1)\(B2*x+c);
    disp(x');
end

3. Lagranz
X = [0 0.8 1.2 1.5 2];
f = @(x) sqrt(1+x);
F = f(X);
x0 = 1.8;
n = length(X);
pol = 0;
for i = 1:n
   L = 1;
   for j = 1:n
      if j~=i
         L = conv(L,[1 -X(j)]) / (X(i)-X(j));
      end
   end
   pol = pol + L*F(i);
end
pol
polyval(pol,x0);

Njutn
X = [0 0.4 0.9 1.2 1.5];
f = @(x) exp(x)./(1+x);  PAZI NA TACKU
F = f(X);
n = length(X);
A = zeros(n,n+1);
A(:,1) = X;
A(:,2) = F;
for j = 1:n-1
      	for i = 1:n-j
        	A(i,j+2) = (A(i+1,j+1)-A(i,j+1))/(X(i+j) - X(i));
     	end
end
disp(A);

4.
f = @(x) sqrt(1 + cos(x));
a = 0;
b = pi/4;
n = 8;
X = linspace(a,b,n+1);
h = (b-a)/n;
p = 4;
F = zeros(n+1,4);
F(:,1) = X;
F(1,2) = f(X(1));
F(n+1, 2) = f(X(n+1));
F(2:2:n,3) = f(X(2:2:n));
F(3:2:n,4) = f(X(3:2:n));
disp(F);

rung E = abs(Ihs - I2hs)/(2^p - 1)
Ihs = h/3*(F(1,2) + F(n+1,2) + 4*sum(F(:,3)) + 2*sum(F(:,4)))
I2hs = (2*h)/3*(sum(F(:,2)) + 4*sum(F(3:4:n,4)) + 2*sum(F(5:4:n,4)))
Ip = h*(F(1,2) + sum(F(:,3)) + sum(F(:,4)))
I2hp = (2*h)*(F(1,2)+sum(F(:,4)));
It = h*((F(1,2) + F(n+1,2))/2 + sum(F(:,3)) + sum(F(:,4)))
I2ht = 2*h*((F(1,2)+F(n+1,2))/2+sum(F(:,4)));

f = log(x+1);
syms x;
df=diff(f)
fplot(df,[0,1])
Ep = h/2*(b-a)*M1
Et = (b-a)/12*h^2*M2
Es = (b-a)/180*h^4*M4