The document discusses two interpolation methods - Newton forward difference method and backward method. It provides the code to calculate the forward difference table using Newton forward difference method. It also provides functions to implement backward interpolation method and Stirling's interpolation formula.

1. Sajid Ali
081220-097
INTERPOLATION Methods:
NEWTON FORWARD DIFFERENCE METHOD:
n = input('nEnter number of data points = ');
h = input('nEnter step size (h) = ')
x(1) = input('nx0 = ');
y(1) = input('y0 = ');
for i=2:n
x(i)=x(i-1)+h;
fprintf('nX%d = %f',i,x(i));
fprintf('ttY%d: ',i);
y(i) = input('');
end
x_reqd = input('nEnter X for which value of Y is sought: ');
s=(x_reqd-x(1))/h;
for i=1:n
diff(i,1)=y(i);
end
%% Calculate Forward Differance Table
for j=2:n
for i=1:n-j+1
diff(i,j)=diff(i+1,j-1)-diff(i,j-1);
end
end
%% Print Forward Differance Table
fprintf('ntXt Forward Differance Table');
for i=1:n
fprintf('n %.4f',x(i));
for j=1:n-i+1
fprintf('t%.4f',diff(i,j));
end
end
ans=y(1);
for i=1:n-1
term=1;
for j=1:i
term=term*(s+j-1)/j;
end
ans=ans+term*diff(1,i+1);
end
Backward Methed:
function Forward()
x=[0;1;2;3;4;5;6];

2. y=[2;3;10;29;66;127;218];
dy=[y(2,1)-y(1,1);y(3,1)-y(2,1);y(4,1)-y(3,1);y(5,1)-y(4,1);y(6,1)-
y(5,1);y(7,1)-y(6,1)];
d2y=[dy(2,1)-dy(1,1);dy(3,1)-dy(2,1);dy(4,1)-dy(3,1);dy(5,1)-
dy(4,1);dy(6,1)-dy(5,1)];
d3y=[d2y(2,1)-d2y(1,1);d2y(3,1)-d2y(2,1);d2y(4,1)-d2y(3,1);d2y(5,1)-
d2y(4,1)];
d4y=[d3y(2,1)-d3y(1,1);d3y(3,1)-d3y(2,1);d3y(4,1)-d3y(3,1)];
d5y=[d4y(2,1)-d4y(1,1);d4y(3,1)-d4y(2,1)];
d6y=[d5y(2,1)-d5y(1,1)];
p=(.5-0)/1;
Y=y(1,1)+(((p*dy(1,1)))+((p*(p-1))/2)*d2y(1,1))+(((p*(p-1)*(p-
2))/6)*d3y(1,1))+(((p*(p-1)*(p-2)*(p-3))/24)*d4y(1,1))+(((p*(p-1)*(p-2)*(p-
3)*(p-4))/120)*d5y(1,1))+(((p*(p-1)*(p-2)*(p-3)*(p-4)*(p-5))/720)*d6y(1,1))
end
Striling
function Forward()
x=[0;1;2;3;4;5;6];
y=[2;3;10;29;66;127;218];
dy=[y(2,1)-y(1,1);y(3,1)-y(2,1);y(4,1)-y(3,1);y(5,1)-y(4,1);y(6,1)-
y(5,1);y(7,1)-y(6,1)];
d2y=[dy(2,1)-dy(1,1);dy(3,1)-dy(2,1);dy(4,1)-dy(3,1);dy(5,1)-
dy(4,1);dy(6,1)-dy(5,1)];
d3y=[d2y(2,1)-d2y(1,1);d2y(3,1)-d2y(2,1);d2y(4,1)-d2y(3,1);d2y(5,1)-
d2y(4,1)];
d4y=[d3y(2,1)-d3y(1,1);d3y(3,1)-d3y(2,1);d3y(4,1)-d3y(3,1)];
d5y=[d4y(2,1)-d4y(1,1);d4y(3,1)-d4y(2,1)];
d6y=[d5y(2,1)-d5y(1,1)];
p=(.5-0)/1;
Y=y(1,1)+(((p*dy(1,1)))+((p*(p-1))/2)*d2y(1,1))+(((p*(p-1)*(p-
2))/6)*d3y(1,1))+(((p*(p-1)*(p-2)*(p-3))/24)*d4y(1,1))+(((p*(p-1)*(p-
2)*(p-3)*(p-4))/120)*d5y(1,1))+(((p*(p-1)*(p-2)*(p-3)*(p-4)*(p-
5))/720)*d6y(1,1))
end