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//Eg-10.1
//pg-430
clear
clc
//Since the interpolating polynomial is of order 3 we have 4 unknown coefficients a0,a1,a2,a3.
//The polynomial finally looks like a3x^3 + a2*x^2 + a1*x + a0 = f(x)
x = [1;2;3;4];
for(i = 1:4)
for(j = 1:4)
A(i,j) = x(i)^(j-1);
end
end
B = [2;3.5;3;4];
T(1:4,1:4) = A;
T(:,5) = B;
//Gauss Elimination
for(i = 2:4)
T(i,:) = T(i,:) - T(1,:)
end
for(i = 3:4)
T(i,:) = T(i,:) - T(i,2)/T(1,2)*(T(2,:));
end
T(4,:) = T(4,:) - T(4,3)/T(3,3)*(T(3,:));
for(i=1:4)
T(i,:) = T(i,:)/T(i,i);
end
for(i = 1:3)
T(4-i,:) = T(4-i,:) - T(4,:)*T(4-i,4);
end
for(i = 1:2)
T(3-i,:) = T(3-i,:) - T(3,:)*T(3-i,3);
end
T(1,:) = T(1,:) - T(2,:);
X = T(:,5);
h = poly(X,'x',"coeff")
disp(X)
disp(h)
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