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

---
 845/CH3/EX3.5/Ex3_5.sce | 50 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100755 845/CH3/EX3.5/Ex3_5.sce

(limited to '845/CH3/EX3.5')

diff --git a/845/CH3/EX3.5/Ex3_5.sce b/845/CH3/EX3.5/Ex3_5.sce
new file mode 100755
index 000000000..653871380
--- /dev/null
+++ b/845/CH3/EX3.5/Ex3_5.sce
@@ -0,0 +1,50 @@
+//Example 3.5
+clc
+clear
+
+A = [5 -2 1; 7 1 -5; 3 7 4];
+B = [4; 8; 10];
+
+n = length (B);
+L = zeros(n,n);         // L = Lower Triangular Matrix Initiation
+U = eye(n,n);           // U = Upper Triangular Matrix Initiation
+
+// LU Decomposition
+for i = 1:n
+    sum1 = zeros(n-i+1,1);
+    for k = 1:i-1
+        sum1 = sum1 + L(i:n,k) * U(k,i);
+    end
+    L(i:n,i) = A(i:n,i) - sum1;
+
+    sum2 = zeros(1,n-i);
+    for k = 1:i-1
+        sum2 = sum2 + L(i,k) * U(k,i+1:n);
+    end
+    U(i,i+1:n) = (A(i,i+1:n) - sum2) / L(i,i);
+end
+
+// Forward Substitution
+D = ones(n,1);
+for i = 1:n
+    sum3 = 0;
+    for k = 1:i-1
+        sum3  = sum3 + L(i,k) * D(k);
+    end
+    D(i) = (B(i) - sum3) / L(i,i);
+end
+
+// Back Substitution
+x = ones(n,1);
+for i = n:-1:1
+    sum4 = 0;
+    for k = i+1:n
+        sum4 = sum4 + U(i,k) * x(k);
+    end
+    x(i) = D(i) - sum4;
+end
+
+disp(strcat(["x1 = ",string(x(1))]))
+disp(strcat(["x2 = ",string(x(2))]))
+disp(strcat(["x3 = ",string(x(3))]))
+
-- 
cgit