matlab lab 6 15.05.2018

lab6.m

f=inline('x.^3+2*x.^2+3','x')
fp=inline('3*x.^2+4*x','x')
n=3;
x=linspace(-2,3,100)

h=x(2)-x(1);

for i=1:100
    df(i)=mr(f,h,n,x(i));
end

    plot(x,df);
    figure (2)
    plot(x,df-fp(x));

function df=mr(f,h,n,x)

for i=1:n
    Q(i,1)=phi(h/2^(i-1));
end

for i=2:n
    for j=2:i
        Q(i,j)=Q(i,j-1)+1/(2^(j-1)-1)*(Q(i,j-1)-Q(i-1,j-1));
    end
end

df=Q(n,n);

function[phi]=phi(h)
phi=(f(x+h)-f(x))/h;
end

end


sistemeliniare.m

A=[0 1 2; 1 0 1; 3 2 1]
b=[8;4;10]

x=Gaussfp(A,b);

function[x]=SubstDesc(A,b)

n=size(A,1);

x(n)=b(n)/A(n,n);

for k=n-1:-1:1
    s=0;
    for j=k+1:n
        s=s+A(k,j)*x(j);
    end
    x(k)=(b(k)-s)/A(k,k);
end
end

function [x]=Gaussfp(A,b)
n=size(A,1)
for k=1:n-1
    for j=k:n
        if A(j,k)~=0;
            p=j;
            break
        end
    end
    if p~=k
        A([p,k],:)=A([k,p],:);
    end
    for l=k+1:n
        A(l,:)=A(l,:)-A(l,k)/A(k,k)*A(k,:);
    end
end
x=SubstDesc(A(1:n,1:n),A(:,n+1));
end