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// EXAMPLE (PG 541)
// Consider a Hilbert matrix of order 3
n=3; // Order of the matrix
A=zeros(n,n); // a symmetric positive definite real or complex matrix.
for i=1:n // Initializing 'for' loop
for j=1:n
A(i,j)=1/(i+j-1);
end
end // End of 'for' loop
A
// Rounding off to 4 decimal places
A = A*10^4;
A = int(A);
A = A*10^(-4);
disp(A) // Final Solution
H = A // Here H denoted H bar as denoted in the text
b = [1 0 0]'
x = H\b
// Rounding off to 3 decimal places
x = x*10^3;
x = int(x);
x = x*10^(-3);
disp(x) // Final Solution
//Now, using elimination with Partial Pivoting, we get the following answers
x0 = [8.968 -35.77 29.77]'
// ro is Residual correction
r0 = b - A*x0
// A*e0 = r0
e0 = inv(A)*r0
x1 = x0 + e0
// Repeating the above operations, we can get the values of r1, x2, e1...
// The vector x2 is accurate to 4 decimal digits.
// Note that x1 - x0 = e0 is an accurate predictor of the error e0 in x0.
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