clear
n = 3; % the order of the polynomial
a = 2.0; % left end of the interval
b = 3.0; % right end of the interval
h = (b – a)/n; % interpolation grid size
t = a:h:b; % interpolation points
f = 1./t; % f(x) = 1./x, This is the function evaluated at interpolation points

%%%% pn(x) = sum f(t_i)l_i(x)
hh = 0.01; % grid to plot the function both f and p
x = a:hh:b;
fexact = 1./x; %exact function f at x
l = zeros(n+1, length(x)); %%%% l(1,:): l_0(x), …, l(n+1): l_n(x)
nn = ones(n+1, length(x));
d = ones(n + 1, length(x));

for i = 1:n+1
for j = 1:length(x)
nn(i,j) = 1;
d(i,j) = 1;
for k = 1:n+1
if i ~= k
nn(i,j) = nn(i,j) * (x(j) – t(k));
d(i,j) = d(i,j) * (t(i) – t(k));
end
end
l(i,j) = nn(i,j)/d(i,j);
end
end

fapp = zeros(length(x),1);
for j = 1:length(x)
for i=1:n+1
fapp(j) = fapp(j) + f(i)*l(i,j);
end
end
En = 0;
Ed = 0;
for i = 1:length(x)
Ed = Ed + fexact(i)^2;
En = En + (fexact(i) – fapp(i))^2;
end
Ed = sqrt(Ed);
En = sqrt(En);
E = En/Ed;
display(E)

plot(x,fexact,’b*-‘)
hold on
plot(x,fapp,’ro-‘ )clear
n = 3; % the order of the polynomial
a = 2.0; % left end of the interval
b = 3.0; % right end of the interval
h = (b – a)/n; % interpolation grid size
t = a:h:b; % interpolation points
f = 1./t; % f(x) = 1./x, This is the function evaluated at interpolation points

%%%% pn(x) = sum f(t_i)l_i(x)
hh = 0.01; % grid to plot the function both f and p
x = a:hh:b;
fexact = 1./x; %exact function f at x
l = zeros(n+1, length(x)); %%%% l(1,:): l_0(x), …, l(n+1): l_n(x)
nn = ones(n+1, length(x));
d = ones(n + 1, length(x));

for i = 1:n+1
for j = 1:length(x)
nn(i,j) = 1;
d(i,j) = 1;
for k = 1:n+1
if i ~= k
nn(i,j) = nn(i,j) * (x(j) – t(k));
d(i,j) = d(i,j) * (t(i) – t(k));
end
end
l(i,j) = nn(i,j)/d(i,j);
end
end

fapp = zeros(length(x),1);
for j = 1:length(x)
for i=1:n+1
fapp(j) = fapp(j) + f(i)*l(i,j);
end
end
En = 0;
Ed = 0;
for i = 1:length(x)
Ed = Ed + fexact(i)^2;
En = En + (fexact(i) – fapp(i))^2;
end
Ed = sqrt(Ed);
En = sqrt(En);
E = En/Ed;
display(E)

plot(x,fexact,’b*-‘)
hold on
plot(x,fapp,’ro-‘ ) clear
n = 3; % the order of the polynomial
a = 2.0; % left end of the interval
b = 3.0; % right end of the interval
h = (b – a)/n; % interpolation grid size
t = a:h:b; % interpolation points
f = 1./t; % f(x) = 1./x, This is the function evaluated at interpolation points

%%%% pn(x) = sum f(t_i)l_i(x)
hh = 0.01; % grid to plot the function both f and p
x = a:hh:b;
fexact = 1./x; %exact function f at x
l = zeros(n+1, length(x)); %%%% l(1,:): l_0(x), …, l(n+1): l_n(x)
nn = ones(n+1, length(x));
d = ones(n + 1, length(x));

for i = 1:n+1
for j = 1:length(x)
nn(i,j) = 1;
d(i,j) = 1;
for k = 1:n+1
if i ~= k
nn(i,j) = nn(i,j) * (x(j) – t(k));
d(i,j) = d(i,j) * (t(i) – t(k));
end
end
l(i,j) = nn(i,j)/d(i,j);
end
end

fapp = zeros(length(x),1);
for j = 1:length(x)
for i=1:n+1
fapp(j) = fapp(j) + f(i)*l(i,j);
end
end
En = 0;
Ed = 0;
for i = 1:length(x)
Ed = Ed + fexact(i)^2;
En = En + (fexact(i) – fapp(i))^2;
end
Ed = sqrt(Ed);
En = sqrt(En);
E = En/Ed;
display(E)

plot(x,fexact,’b*-‘)
hold on
plot(x,fapp,’ro-‘ ) chebyshev, points MATLAB Answers — New Questions

​