From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

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 75/CH8/EX8.8/ex_8.sce | 47 +++++++++++++++++++++++++++++++++++++++++++++++
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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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