philips.m

philips光滑化方法求解基于反演问题

clear all
r=0.1;
i=1;
for x=0:0.1:5
    G(i)=(5.5-x).*exp(x)-0.5.*exp(-x)+0.5*(sin(10*x+1)+cos(23*x+2));
    j=1;
    for y=0:0.1:5
        K(i,j)=exp(-(abs(x-y)));
        A(i,j)=K(i,j)*0.1;
        j=j+1;
    end
    i=i+1;
end  
AA=inv(A);
D=zeros(length(AA)+4,length(AA));
D(3:length(D)-2,:)=AA;
for j=1:length(AA)
    D(1,j)=-D(3,j);
    D(length(D),j)=-D(length(D)-2,j);
    D(2,j)=0;
    D(length(D)-1,j)=0;
end
i=1;
for x=0:0.1:5
    j=1;
    for y=0:0.1:5
        B(i,j)=D(i,j)-4*D(i+1,j)+6*D(i+2,j)-4*D(i+3,j)+D(i+4,j);
        j=j+1;
    end
    i=i+1;
end
C=(A+r*B);
F=C\G';
E=-r*B*F;
e=E'*E
x=0:0.1:5;
y=0:0.1:5;
subplot(2,2,1)
plot(F,':+');
title('Philips方法求得的曲线')
xlabel('x')
ylabel('y')
subplot(2,2,2)
plot(exp(y));
title('理论曲线')
xlabel('x')
ylabel('y')
subplot(2,2,3)
plot(F,':+');
hold on
plot(exp(y));
hold off
title('两图形对比图')
xlabel('x')
ylabel('y')