% Tschebyscheff and Equi-interval method for interpolation program % Function f(x)=1/(25*x^2)
clear all; %xe equi-interval %xc tschebyscheff x=-1:0.01:1; N=length(x); num = [5 9 13];
for i=1:3 xe = -1:2/(num(i)-1):1; for k=1:num(i) fe(k) = 1 / ( 1 + 25 * xe(k) * xe(k) ); % equi-interval function xc(k) = cos((2*(k-1)+1)*pi/(2*num(i))); % tschebyscheff point fc(k) = 1 / ( 1 + 25 * xc(k) * xc(k) ); % tschebyscheff function end for n=1:N
f(n) = 1 / ( 1 + 25 * x(n) * x(n) ) ;
pe(i,n)=0.0;
pc(i,n)=0.0;
for jj=1:num(i)
l1(jj)=1.0;
l2(jj)=1.0;
% Lagrange interpolation
for ii=1:num(i)
if ii ~= jj
l1(jj) = ( l1(jj) * ( x(n) - xe(ii) ) ) / ( xe(jj) - xe(ii) );
l2(jj) = ( l2(jj) * ( x(n) - xc(ii) ) ) / ( xc(jj) - xc(ii) );
end
end
pe(i,n) = pe(i,n) + fe(jj) * l1(jj);
pc(i,n) = pc(i,n) + fc(jj) * l2(jj);
end
if i ==1
pe4(n) = pe(1,n);
pc4(n) = pc(1,n);
elseif i==2
pe8(n) = pe(2,n);
pc8(n) = pc(2,n);
else
pe12(n) = pe(3,n);
pc12(n) = pc(3,n);
end
end
end
% graph plot figure(1); plot(x,f,x,pe4,x,pe8,x,pe12); legend('F(x)','P4(x)','P8(x)','P12(x)'); AXIS([-1 1 -3.7 1.5]) xlabel('x'); ylabel('Function F(x) and Pn(x)'); title(['interpolated graph by equi-interval method F(x) ‚Æ Pn(x)']);
figure(2); plot(x,f,x,pc4,x,pc8,x,pc12); legend('F(x)','P4(x)','P8(x)','P12(x)'); AXIS([-1 1 -0.2 1.1]) xlabel('x'); ylabel('Function F(x) and Pn(x)'); title(['interpolated graph by tschebyscheff point F(x) ‚Æ Pn(x)']);
